EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
2nd Edition
ISBN: 9781337772020
Author: Stewart
Publisher: VST
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Chapter 2.6, Problem 38E
To determine
To show: One family of the curves are orthogonal trajectories to the other family.
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Question 1. (10 points)
A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by
dV
=
1.45V(2 In(V+1)).
dt
(a) (4 pts) Find all the equilibria and determine their stability using the stability condition.
(b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of
f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable.
(c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain
in biological terms what happens to the size of each of these tumours at time progresses.
For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.
Question 2: (10 points) Evaluate the definite integral.
Use the following form of the definition of the integral to evaluate the integral:
Theorem: Iff is integrable on [a, b], then
where Ax = (ba)/n and x₂ = a + i^x.
You might need the following formulas.
IM³
L² (3x²
(3x²+2x-
2x - 1)dx.
n
[f(z)dz lim f(x)Az
a
n→∞
i=1
n(n + 1)
2
n
i=1
n(n+1)(2n+1)
6
Chapter 2 Solutions
EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
Ch. 2.1 - (a) Find the slope of the tangent line to the...Ch. 2.1 - (a) Find the slope of the tangent line to the...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - Find an equation of the tangent line to the curve...Ch. 2.1 - (a) Find the slope of the tangent to the curve y =...Ch. 2.1 - (a) Find the slope of the tangent to the curve...Ch. 2.1 - The graph shows the position function of a car....Ch. 2.1 - Shown are graphs of the position functions of two...
Ch. 2.1 - If a ball is thrown into the air with a velocity...Ch. 2.1 - If an arrow is shot upward on the moon with a...Ch. 2.1 - The displacement (in meters) of a particle moving...Ch. 2.1 - The displacement (in meters) of a particle moving...Ch. 2.1 - Prob. 15ECh. 2.1 - Find an equation of the tangent line to the graph...Ch. 2.1 - If an equation of the tangent tine to the curve y...Ch. 2.1 - If the tangent line to y= f(x) at (4, 3) passes...Ch. 2.1 - Sketch the graph of a function f for which f(0) =...Ch. 2.1 - Sketch the graph of a function g for which g(0) =...Ch. 2.1 - If f(x) = 3x2 x3 , find f'(l) and use it to find...Ch. 2.1 - Prob. 22ECh. 2.1 - (a) If F(x) = 5x/(l + x2), find F'(2) and use it...Ch. 2.1 - Prob. 24ECh. 2.1 - Find f'(a). f(x) = 3x2 4x + 1Ch. 2.1 - Find f'(a). f(t) = 2t3 + tCh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Each limit represents the derivative of some...Ch. 2.1 - Each limit represents the derivative of some...Ch. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - 3136 Each limit represents the derivative of some...Ch. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - The number N of US cellular phone subscribers (in...Ch. 2.1 - The number N of locations of a popular coffeehouse...Ch. 2.1 - Prob. 41ECh. 2.1 - If a cylindrical tank holds 100,000 gallons of...Ch. 2.1 - The cost of producing x ounces of gold from a new...Ch. 2.1 - The number of bacteria after r hours in a...Ch. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - The graph shows the influence of the temperature T...Ch. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.2 - Use the given graph to estimate the value of each...Ch. 2.2 - Use the given graph to estimate the value of each...Ch. 2.2 - Match the graph of each function in (a)(d) with...Ch. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Trace or copy the graph of the given function .f....Ch. 2.2 - Shown is the graph of the population function P(t)...Ch. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Find the derivative of the function using the...Ch. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - The unemployment rate U(t) varies with time. The...Ch. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - The graph of f is given. State, with reasons, the...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Use the definition of a derivative to find f'(x)...Ch. 2.2 - Prob. 42ECh. 2.2 - If f(x) = 2x2 x3, find f'(x), f"(x), f'"(x), and...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Where is the greatest integer function f(x) = [[ x...Ch. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.3 - Differentiate the function. f(x) = 240Ch. 2.3 - Differentiate the function. f(x)=2Ch. 2.3 - Differentiate the function. f(t)=223tCh. 2.3 - Differentiate the function. F(x)=34x8Ch. 2.3 - Prob. 5ECh. 2.3 - Differentiate the function. f(t) = 1.4t5 2.5t2+...Ch. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Differentiate the function. B(y) = cy6Ch. 2.3 - Differentiate the function. A(s)=12s5Ch. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Differentiate the function. y=x(x1)Ch. 2.3 - Prob. 17ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 18ECh. 2.3 - Differentiate the function. z=Ay10+BcosyCh. 2.3 - Prob. 22ECh. 2.3 - Differentiate the function. y=x2+4x+3xCh. 2.3 - Differentiate the function. y=sin2+cCh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 55ECh. 2.3 - Find the points on the curve y = 2x3 + 3x2 12x +...Ch. 2.3 - Prob. 37ECh. 2.3 - Show that the curve y = 6x3 + 5x 3 has no tangent...Ch. 2.3 - Find an equation of the tangent line to the curve...Ch. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 65ECh. 2.3 - Prob. 64ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 67ECh. 2.3 - Prob. 66ECh. 2.3 - For what values of a and b is the line 2x + y = b...Ch. 2.3 - Prob. 68ECh. 2.3 - Prob. 69ECh. 2.3 - Draw a diagram showing two perpendicular lines...Ch. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - If a ball is thrown vertically upward with a...Ch. 2.3 - If a rock is thrown vertically upward from the...Ch. 2.3 - The position function of a particle is given by s...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 51ECh. 2.3 - The cost function for production of a commodity is...Ch. 2.4 - Find the derivative of f(x) = (1 + 2x2)(x x2) in...Ch. 2.4 - Find the derivative o f the function...Ch. 2.4 - Differentiate. g(t)=t3costCh. 2.4 - Differentiate. f(x)=xsinxCh. 2.4 - Differentiate. g(x)=1+2x34xCh. 2.4 - Differentiate. G(x)=x222x+1Ch. 2.4 - Differentiate. h()=csccotCh. 2.4 - Differentiate. J(v) = (v3 2v)(v4 + v2)Ch. 2.4 - Prob. 5ECh. 2.4 - Differentiate. y=sincosCh. 2.4 - Differentiate. y=x31x2Ch. 2.4 - Differentiate. y=x+1x3+x2Ch. 2.4 - Differentiate. y=v32vvvCh. 2.4 - Differentiate. g(t)=ttt1/3Ch. 2.4 - Differentiate. f(t)=2t2+tCh. 2.4 - Differentiate. y=x1x+1Ch. 2.4 - Differentiate. f()=sec1+secCh. 2.4 - Differentiate. y=1secxtanxCh. 2.4 - Prob. 24ECh. 2.4 - Differentiate. f(x)=xx+cxCh. 2.4 - Find an equation of the tangent line to the given...Ch. 2.4 - Find an equation of the tangent line to the given...Ch. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - If f and g are the functions whose graphs are...Ch. 2.4 - Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F...Ch. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 7ECh. 2.4 - Differentiate. y = 2 sec x csc xCh. 2.4 - Prob. 19ECh. 2.4 - Differentiate. y=cosx1sinxCh. 2.4 - Prob. 23ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Find an equation of the tangent line to the curve...Ch. 2.4 - Prob. 30ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 40ECh. 2.4 - A mass on a spring vibrates horizontally on a...Ch. 2.4 - Prob. 52ECh. 2.4 - Prob. 36ECh. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Write the composite function in the form f(g(x))....Ch. 2.5 - Find the derivative of the function. F(x) = (x4 +...Ch. 2.5 - Find the derivative of the function. F(x) = (4x ...Ch. 2.5 - Find the derivative of the function. F(x)=12xCh. 2.5 - Find the derivative of the function....Ch. 2.5 - Prob. 11ECh. 2.5 - Find the derivative of the function. f(t)=1+tant3Ch. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Find the derivative of the function. f(x) = (2x ...Ch. 2.5 - Find the derivative of the function. g(x) = (x2 +...Ch. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Find the derivative of the function. y=(x2+1x21)3Ch. 2.5 - Find the derivative of the function. f(s)=s2+1s2+4Ch. 2.5 - Find the derivative of the function. y=sin(xcosx)Ch. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Find the derivative of the function. y = cot2(sin...Ch. 2.5 - Prob. 36ECh. 2.5 - 742 Find the derivative of the function. 37....Ch. 2.5 - Find the derivative of the function. y=x+x+xCh. 2.5 - Prob. 39ECh. 2.5 - 742 Find the derivative of the function. 40....Ch. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - A table of values for f, g, f, and g is given. (a)...Ch. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5 - Prob. 75ECh. 2.5 - Prob. 76ECh. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - Prob. 67ECh. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - Air is being pumped into a spherical weather...Ch. 2.5 - Prob. 72ECh. 2.5 - Prob. 71ECh. 2.5 - Prob. 74ECh. 2.5 - Use the Chain Rule to show that if is measured in...Ch. 2.5 - Prob. 78ECh. 2.5 - Prob. 77ECh. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - (a) Find y by implicit differentiation. (b) Solve...Ch. 2.6 - Find dy/dx by implicit differentiation. x3 + y3 =...Ch. 2.6 - Find dy/dx by implicit differentiation. 2x3 + x2y ...Ch. 2.6 - Prob. 5ECh. 2.6 - Find dy/dx by implicit differentiation. y5 + x2y3...Ch. 2.6 - Find dy/dx by implicit differentiation. 11. y cos...Ch. 2.6 - Find dy/dx by implicit differentiation. 12....Ch. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Find dy/dx by implicit differentiation. x+y=1+x2y2Ch. 2.6 - 3-16 Find dy/dx by implicit differentiation. 13....Ch. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Find dy/dx by implicit differentiation. 20....Ch. 2.6 - Prob. 17ECh. 2.6 - If g(x) + x sin g(x) = x2, find g(0).Ch. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 19ECh. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 22ECh. 2.6 - Use implicit differentiation to find an equation...Ch. 2.6 - Prob. 24ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Find the points on the lemniscate in Exercise 23...Ch. 2.6 - Show by implicit differentiation that the tangent...Ch. 2.6 - Show that the sum of the x-and y-intercepts of any...Ch. 2.6 - Prob. 41ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 49ECh. 2.6 - Prob. 50ECh. 2.7 - Prob. 1ECh. 2.7 - (a) If A is the area of a circle with radius r and...Ch. 2.7 - Prob. 3ECh. 2.7 - The length of a rectangle is increasing at a rate...Ch. 2.7 - A cylindrical tank with radius 5 m is being filled...Ch. 2.7 - The radius of a sphere is increasing at a rate of...Ch. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - A particle is moving along a hyperbola xy = 8. As...Ch. 2.7 - Prob. 13ECh. 2.7 - (a) What quantities are given in the problem? (b)...Ch. 2.7 - (a) What quantities are given in the problem? (b)...Ch. 2.7 - (a) What quantities are given in the problem? (b)...Ch. 2.7 - Two cars start moving from the same point. One...Ch. 2.7 - A spotlight on the ground shines on a wall 12m...Ch. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 24ECh. 2.7 - A trough is 10 ft long and its ends have the shape...Ch. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Prob. 31ECh. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 37ECh. 2.7 - A lighthouse is located on a small island 3 km...Ch. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2.7 - Prob. 41ECh. 2.7 - Prob. 42ECh. 2.8 - Find the linearization L(x) of the function at a....Ch. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 10ECh. 2.8 - 7-10 Verify the given linear approximation at a =...Ch. 2.8 - Prob. 8ECh. 2.8 - Prob. 18ECh. 2.8 - Prob. 17ECh. 2.8 - Let y = tan x. (a) Find the differential dy. (b)...Ch. 2.8 - Let y = tan x. (a) Find the differential dy. (b)...Ch. 2.8 - Prob. 11ECh. 2.8 - Prob. 14ECh. 2.8 - Use a linear approximation (or differentials) to...Ch. 2.8 - Prob. 13ECh. 2.8 - Prob. 15ECh. 2.8 - Prob. 16ECh. 2.8 - Prob. 21ECh. 2.8 - Prob. 22ECh. 2.8 - The circumference of a sphere was measured to be...Ch. 2.8 - Prob. 24ECh. 2.8 - One side of a right triangle is known to be 20 cm...Ch. 2.8 - Prob. 25ECh. 2.8 - When blood flows along a blood vessel, the flux F...Ch. 2.8 - Prob. 28ECh. 2.8 - Prob. 29ECh. 2.8 - Suppose that we dont have a formula for g(x) but...Ch. 2 - Prob. 1RCCCh. 2 - Prob. 2RCCCh. 2 - Prob. 4RCCCh. 2 - Prob. 3RCCCh. 2 - Prob. 5RCCCh. 2 - Prob. 6RCCCh. 2 - Prob. 7RCCCh. 2 - Prob. 1RQCh. 2 - Prob. 8RQCh. 2 - Determine whether the statement is true or false....Ch. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 63RECh. 2 - Prob. 7RECh. 2 - Prob. 9RECh. 2 - Prob. 8RECh. 2 - Prob. 8RCCCh. 2 - Prob. 9RCCCh. 2 - Prob. 10RCCCh. 2 - Prob. 11RCCCh. 2 - Prob. 2RQCh. 2 - Prob. 3RQCh. 2 - Prob. 4RQCh. 2 - Prob. 5RQCh. 2 - Prob. 6RQCh. 2 - Prob. 12RQCh. 2 - Prob. 7RQCh. 2 - Prob. 11RQCh. 2 - Prob. 9RQCh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 19RECh. 2 - Prob. 33RECh. 2 - Prob. 1RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 18RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 24RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 39RECh. 2 - Prob. 35RECh. 2 - Prob. 32RECh. 2 - Prob. 34RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - 70. If f and g are the functions whose graphs are...Ch. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 57RECh. 2 - Prob. 56RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 65RECh. 2 - Prob. 64RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Evaluate limx01+tanx1+sinxx3.Ch. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RE
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- For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardFor the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardOpen your tool box and find geometric methods, symmetries of even and odd functions and the evaluation theorem. Use these to calculate the following definite integrals. Note that you should not use Riemann sums for this problem. (a) (4 pts) (b) (2 pts) 3 S³ 0 3-x+9-dz x3 + sin(x) x4 + cos(x) dx (c) (4 pts) L 1-|x|dxarrow_forward
- An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $48 per mile to lay, the second section runs from point Q to point R and costs $54 per mile, the third runs from point R to point S and costs $44 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. Please show your answers to 4 decimal places. 2 Miles x = 1 Mile R 10 miles miles y = milesarrow_forwardAn open-top rectangular box is being constructed to hold a volume of 150 in³. The base of the box is made from a material costing 7 cents/in². The front of the box must be decorated, and will cost 11 cents/in². The remainder of the sides will cost 3 cents/in². Find the dimensions that will minimize the cost of constructing this box. Please show your answers to at least 4 decimal places. Front width: Depth: in. in. Height: in.arrow_forwardFind and classify the critical points of z = (x² – 8x) (y² – 6y). Local maximums: Local minimums: Saddle points: - For each classification, enter a list of ordered pairs (x, y) where the max/min/saddle occurs. Enter DNE if there are no points for a classification.arrow_forward
- Suppose that f(x, y, z) = (x − 2)² + (y – 2)² + (z − 2)² with 0 < x, y, z and x+y+z≤ 10. 1. The critical point of f(x, y, z) is at (a, b, c). Then a = b = C = 2. Absolute minimum of f(x, y, z) is and the absolute maximum isarrow_forwardThe spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.arrow_forwardFind the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forward
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