Discussion Unit Write an example of a function whose derivative can be found by using the following rules: a) Product rule and special function differentiation rules b) Power rule, quotient rule, and chain rule Chain rule twice d) Implicit differentiation and special function differentiation rule

Q: Say that L1 is the line through the points (1, 2, 6) and (2, 4, 8). Say that L2 is the line of…

A:

Q: sinh(2ln(c))= (A) + 1 2c² (B) c² - 2/2 (C) 2-2/2/2 2c² 1 (D) c- ! C (E) 0 1:37 A

A:

Q: Rewrite the quadratic function in transformation form. h(x) = 2x² + 8x - 5 h(x) = Give the vertex. (…

A: Here we have to write inthe standard form

Q: If g(x) = 2 + x + ex, find g-¹(3).

A:

Q: r(t) = (cos πt, 2t, sin 2πt), from (1, 0, 0) to (1, 4, 0)

A:

Q: Using the Inverse of a Matrix In Exercises 19-26, use an inverse matrix to solve each system of…

A: Given 3x1+2x2=1 x1+4x2=-3

Q: Find the limit of 6x+2 lim 2+00 102-√36x². I lim z++∞ 10x 6x + 2 36x² - 2

A:

Q: Verify if the primitive y = c₁sin (x) + C₂X defines the corresponding differential equation dy X +y…

A:

Q: Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.…

A: Fluid force=∫abρh(y)d(y)dywhere ρ is the density of liquid            h(y)  horizontal length of the…

Q: A toll bridge charges $1.00 for passenger cars and $2.25 for other vehicles. Suppose that during…

A: Topic- Linear equations we are given Toll bridge charge per passenger car=$1.00 Toll bridge charge…

Q: nd the average rate of change of the given function between the following pairs of x-values. (Round…

A:

Q: -10 -8 Challenge #7: Sketch the derivative of the function, h(x). T √ -6 -4 S -2 -6- 4 --2- 0 -2 -4.…

A: when x<-2h(x) is constant

Q: f and g are continuous functions with f(3) = 5 and lim[2f(x) – g(x)] = 4, find x-3 g(3). g(3): =

A:

Q: Find an equation for a plane P that: meets the x axis at the point where x = a, meets the y axis at…

A: Here plane passing through the points (a,0,0) , (0,b,0) and (0,0,c) We know that equation of plane…

Q: Determine the intervals over which the function shown below is continuous. Enter your answer in…

A:

Q: Find the general solution of the following equation.

A: Find the general solution of  dy/dx= yex

Q: Question How much work does it take to pump all the water over the top edge of a cylindrical tank of…

A:

Q: The population of deer in a forest can be modeled by: P(x) = (630x +2960) / (3x+8) x is the number…

A: The population of deer in a forest can be modeled by: P(x) = (630x +2960) / (3x+8) x is the number…

Q: 16. dy dx = 4e-3x, y = 2 when x = 0 0

A:

Q: Find the absolute minimum value of the function f(x) shown below. Give just the value as your…

A: According to the given graph Absolute minima is the minimum value of the function

Q: a. f(x) = √x 2 b. g(x) = √x²

A:

Q: 6. Find lim1F(t), where r(t) = 1² In (2t - 1) 1' 2022-t (1=1) 1/1₁ eve).

A: Answer and explanation is given below...

Q: Given y=In(2-4x2) + 2e-3x+9x, then y'= O True O False 8x 2-4x² 6 -3x +9

A:

Q: 1) Ax B×C 2) AXBXB 3) BX AXC 4) (A-B) x C A = {1,2}, B = {a}, C = {a, ß}

A: Given, A = {1, 2}, B = {α}, C = {α, β}

Q: In a frequency distribution table if the last class interval is 18– 34, then the class size will be:…

A:

Q: Simplify 3π2 sinh (πx) - π2 cosh (πx) - 3 sinh (πx) + cosh (πx) = 0 on the interval (0,1).

A:

Q: 22 (2y + xy² ) = √7 + (y)²

A: The order of a differential equation is defined to be that of the highest order derivative it…

Q: 3. Find the plane that satisfies the following conditions: (a) The plane that passes through the…

A: Equation of planes passing through points x1,y1,z1,x2,y2,z2,x3,y3,z3…

Q: 1.) (3tz - z²)dt + t(t − z)dz = 0 -

A:

Q: 1. Solve d²y 1 1 1²2-69² +9y = 6³² (√2-²2²-27) dy 6. dx² dx

A:

Q: Challenge #4: Sketch the DERIVATIVE of the graph shown here. T -8 √ 8 S 4 -4 4 K 8

A: see below the answer

Q: Find f'(x) by using the definition of the derivative. [Hint: Use (x + h)5 = x5 + 5x¹h + 10x³h² +…

A:

Q: Given f(t) = sin² t + cos² t g (t) = sec² t - tan² t evaluate f(T) + g(n) B

A: Solve the following

Q: Given the graph of y = f(x) shown below, what is the graph of y = -f(x)? N 6 Un P 3 N…

A: Given a graph of the function

Q: b) h(x) = 5e cos(x)

A:

Q: Kite. Camille flies her kite at an angle of 55° to the ground. If she has used 65 feet of string,…

A:

Q: (A) If y = 5x x² - 4 dy dx dy dx dy dx dy then = dx −5x2 — 20 (x² - 4)² 5x2 – 20 (x²-4)² −5x2 +20…

A:

Q: iF f (x-j) = 2x4 - x³ - 2x² + + X Find the value of f($)

A:

Q: 2. Solve each problem : (a) Find an equation of the line that passes through the point (-3, 4, 2)…

A: I have appended the formula used in the solution part

Q: Using the information provided, which of the following is a conjecture could be proposed from the…

A: Using the information provided, which of the following is a conjecture could be proposed from the…

Q: Given the graph f(x) = || shift the two movable dots to display the following function:…

A: The graph of f(x) = |x| is given as

Q: A tank of cylindrical shape originally contains 180 liters of water and has 5 grams of salt (the…

A: This is a linear differential equation problem. see below the answer and calculation

Q: 3. Find the curvature of the following: Give exact values only a) r(t) = (2t, t³,t²) at t = 1

A: The formulas of curvature are as follows

Q: If g'(0) = 7 and f(x) = 2g(x) - 4ex - x² + 3x, what is f'(0) [A] 13 [B] 11 [C] 14 [E] 17-4e [D] 17-e

A:

Q: Use the graph of f(x) shown below to determine each of the following limits. Provide your answer…

A:

Q: the average value have of the function h on the given interva In(u) U h(u) = [1, 3]

A: Given query is to find the average value of the function.

Q: Use the given graph of the function to find the x-values for which f is discontinuous. 1,0 1,0…

A: Topic- Discontinuity of a function A function is discontinuous at a point if there is a jump in the…

Q: Shown is a graph of g(x). Sketch a graph of g(x + 2). 5 4

A: The given graph of g(x) is shown:

Q: Find the value of the limit: lim X-8 √√5x² + x² +1 6 -9 X C

A: Solve for the limit

Q: 3. xy' = y + 2/ху ху У+

A: #3