Evaluate the integral. (Remember the constant of integration.) [4x²√x+c dx 3²/3x6 + 26 + cx + C X

Q: 2) Show that: cos (0) sin (0) – sin B (6)) (*) = ( cos( 2 ||7p|| cos (0 - a) -|||| sin (0-a), -as))

A: PROOF IS MENTIONED CLEARLY IN THE EXPLANATION BOX.Explanation:

Q: Find dy. y=x² (13 - 1 1) 8 dy = (Simplify your answer.)

A:

Q: 5 Let f(x) = 4 + 12 cos(7x) and g(x) = 6+3x a. Find the composite function f(g(x)) and give its…

A:

Q: For the curve given by r(t) = (5 sin(t), -3t, -5 cos(t)), Find the unit tangent T(t) = (000) Find…

A:

Q: 2. If the portion of y 2 between x = 0 and x = 4 is rotated about the x-axis, what would be the…

A: Given that the region is bounded by the curve  between The surface area of the revolution about…

Q: The following rational function models the speed v(t), in miles per hour (mph), of a dragster 5…

A:

Q: Use logarithmic differentiation to find the derivative of the function. (5x +1) 5 (x4 - 8)6 Y =

A: The given function equation

Q: In this problem, p is the price per unit in dollars and q is the number of units. If the weekly…

A:

Q: Evaluate the double integral: 2 So So ² + ²3/2 dy dr da

A: The given integral

Q: velocity (ft/min) It I 9 time (minutes)

A:

Q: Find the exact area of the region bounded by the given curves. Show a detailed sketch with the…

A: To find the exact are of the region bounded by the given curves.

Q: Test for convergence or divergence with the Direct Comparison Test.

A: The answer is given below.Explanation:

Q: M 6. Use Partial Fractions to determine the e 5 cx = (A₂+B А dx x-3 X+2 1 (x-3)(x+2)

A:

Q: 97. To determine the value of the definite integral: 3 x - 3 x² - 6x + 10 a. Complete the square of…

A:

Q: A rectangle is bounded by the parabola defined by y=x², the x-axis, and the line x = 6 as shown in…

A: A rectangle is bounded by the parabola defined by , the x-axis, and the line as shown in the figure.…

Q: Please help

A: The objective of this question is to find the direction in which the airplane should fly. This can…

Q: Compute f(g(x)), where f(x) = x and g(x) = 8x - 5. d dx To compute f(g(x)), first find f'(x) and…

A: Given Formulas we use:

Q: Calculate r' (t) and T(t), where 18.8.8 r'(t) = ( T(t) = ( r(t) = (5t - 7,- (5+5t), 6 + 5t).

A:

Q: Let y^3-8y+x^2=8. Use implicit differentiation to find the derivative. Find the tangent line at…

A: The equation of the tangent line of the function y= f(x) at  (x0,y0) is           y-y0= f'(x0)(x-x0)

Q: Q/Find the Integral of the following: Inx 1- Not: log₂x In2 log,x X -dx 2- fix dx 1+e dx

A: To evaluate the following integrals.

Q: Both the magnitude and the direction of the force on a crankshaft change as the crankshaft rotates.…

A: The objective of this question is to calculate the magnitude of the torque on a crankshaft given the…

Q: Find the limit, if it exists, or type N if it does not exist. 5zex² + y² lim (x,y,z)→(1,3,2) x² +…

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Remember the constant of…

A:

Q: 3x √x +4 S dx (f) S 1 x(lnx)³ dx π/4 tan³ x cos³x (1) S™ dx

A:

Q: 28 Mr. Durham bought 160 fluid ounces of plant food for his garden. He used 1 cup of plant food to…

A: Mr. Durham bought 160 fluid ounces of plant food for his garden. He used 1 cup of plant food to…

Q: Find the derivative of f(x)= x5 - 7x² + 8x.

A:

Q: To find the arclength of y = 2x²-1 from x = 0 to x = 4, which is the correct integral? 4 = Sº OL=…

A:

Q: (A) find the critical numbers of f, if any (B) find the open intervals on which the function is…

A:

Q: Solve the given initial value problem. y'' + 2y' = 0; y(0)= -1, y'(0) = -10 The solution is y(t)=₁

A:

Q: Consider the following. v = sin(4s² - 3t²) Find the first partial derivatives. Vt = = Find all the…

A:

Q: In this problem, p is in dollars and g is the number of units. (a) Find the elasticity of the demand…

A:

Q: Find if the series converges or diverges.

A: The series ∑k=1∞​k3+1k2​ diverges.Explanation:To determine the convergence or divergence of the…

Q: 7. Give three reasons why a function might not be differentiable at a particular value of x.

A: we will give three reasons why a function might not be differentiable at a particular value of 'x'.

Q: A force with magnitude 15 N acts directly upward from the xy-plane on an object with mass 3 kg. The…

A:

Q: At how many points on the interval [0, π] does f(x) = sinx + sin2x satisfy the Mean Value Theorem?

A:

Q: The reaction R to an injection of a drug is related to the dosex (in milligrams) according to the…

A:

Q: Find the equation of the tangent plane to the surface z = 4y² – 16x² at the point (-4,-2,-240). Z=…

A:

Q: Find the average value of the function f(x) = 22 sin(x) over the interval [0, π]. NOTE: Enter an…

A:

Q: · ƒ (x) = Determine the general tangent slope to the curve = √x +3.

A: The objective of this question is to find the slope of the tangent line to the curve defined by the…

Q: 21. Find a and b such that [-1, a, 6] and [b, 8,12] are collinear. 22. Determine the area of AABC…

A:

Q: ले f(x) = 2/3 - 4

A: The given function is

Q: IT cotdx

A:

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: For the equation given, find ਦੇ ਚ dy 21² (2y-x) 2-x dx 7xy? - 7x?v = 5

A:

Q: a 2 (x-1)² + (y +3) ² = 16 Make a graph, Use at least 4 points 7 Report domain and range. 2 Solve…

A:

Q: Write an equation for the function whose graph is shown to the right. The graph shows a…

A: The shape of this graph matches a parabola, which is a rounded curve that opens upwards or downwards…

Q: 1. For each of the sequence (an} below, determine if the sequence an converges or diverges, and find…

A: The nth term of given sequence(b) (d)

Q: Use the definition to find the Taylor series (centered at c) for the function. f(x) = ex c = 0

A: The given function isThe centered value is

Q: The radius of a circular oil slick expands at a rate of 7 m/min. (a) How fast is the area of the oil…

A: we are given that the rate of increasing of the radius of a circular oil slick is 7m/min and we need…

Q: One method of slowing the growth of an insect population without using pesticides is to introduce…

A: