Let F(x) = f(g(x)), g(2) = -2, g'(2) = 4, f'(2) = 5, and f'(-2) = 7. Find the value of F'(2). Let F(x) = f(f(x)), f(2)= -2, f'(2) = -5, and f'(-2) = 8. Find the value of F'(2).

Q: f(x, y) = 'r cos(y) + y(e² − 1), x‡0 xy 0 x = 0.

A:

Q: Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the…

A: According to the guidelines, we are instructed to answer 1 question or 3 sub question,the others can…

Q: 47-48 Find equations of the tangent line and normal line to the curve at the given point. 47. y =…

A:

Q: Find the derivative of the vector function r(t) = (tsin t, t^2 , t cost)

A:

Q: Consider the following revenue function, where ? is measured in dollars. R(x)=110x-0.1x^2 a. Use…

A: Consider the following revenue function, where R(x) is measured in dollars. R(x)=110x-0.1x^2 a. Use…

Q: The eigenvalues of the matrix 139 - 84 240 145 (a) Find an eigenvector corresponding to X₁ = 1 X1 =…

A:

Q: I. Evaluate the following integrals by substitution. Show your complete solution 1. S (3x + 5)12dx…

A:

Q: Given the relation x³z² + sin(3xz - 2y) - 3√9+7x3 = 5y -23 implicitly defines z as a differentiable…

A:

Q: 1. JC y = f(x) is transformed to g(x) = 3 f (2x – 6) + 9. The domain and the range of each function…

A: Solving

Q: ·SS v₂ Vx (2yi) •n do where S is the hemisphere x² + y² + z² = 9, z≥ 0. Use the normal vectors…

A:

Q: the curve x=l-5¢, y=4€²-1 (0=ts) lengin find the arcC kngth of the curve x=1-. (ux calculator to…

A: This question is based on length of a parametric curve calculated using definite integral.

Q: For what values of x does the series converge conditionally? Σ (-1)^(4x+7)" n=0 OA. x = -2 3 OB. X=…

A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

Q: Use the second derivative test to find the location of all local extrema in the interval (2) for the…

A: We can solve as follows

Q: y varies inversely as the fourth root of x and when x = 81, y = 10. What would be y when x=44. Round…

A:

Q: Find the critical points of the function f(x) = 2²-25 x² + x - 30 Use a comma to separate multiple…

A:

Q: Evaluate (1 + i)(¹ - i). (1

A:

Q: f(x)=x√ 36 = x² ntercepts (x, y) = (x, y) = (x, y) = elative minimum (x, y) = elative maximum (x, y)…

A:

Q: Determine whether the series converges absolutely, converges conditionally, ges. 4n Σ(-1)", n³+1 n=2

A: Use alternating series test for checking the convergence .

Q: Find the length of the curve r(t) = e³t cos(t), y(t) = et sin(t) for 0 < t < 10. Give an exact…

A:

Q: For what values of x does the series converge conditionally? 5x Σ n! n=1 1 O A. x= -7 5 OB. X=0 1…

A:

Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

A:

Q: Find the area of the shaded region. 2+ 1 -1- |-3+ 2 3 square units y=x-2 y=√x

A:

Q: Consider the function f(x) below. At what value(s) of x are the inflection points? Enter answer…

A:

Q: +² = x² dx

A: We have to solve the given differential equation

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

A:

Q: ICLO-3 Use the graph to ist() de.x) dx and S(x) dx in order, from smallest to largest 05 0 0.5 52 25…

A: Here, the curve is above the x-axis for [0,1] and the curve is below the x-axis for [1,2] &amp;…

Q: 1 dx x+1 1

A: Evaluate improper integral

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = , y =…

A:

Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.

Q: Question 1: Find the Laplace transform of the given functions by using the table of Laplace…

A:

Q: ∞ -1. Σ(-1)" n=1 n! 2"

A:

Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

A: Volume

Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

A:

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 13 ft/s. At what rate is the angle…

A:

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A:

Q: Select the conic section represented by the equation. 3x 2 + 2x - 5y + 7 = 0 line hyperbola circle…

A:

Q: 5. Does the function f(x) = e2x - 2x have any points of inflection? Justify your answer.

A:

Q: Let f(x) = 25 x The slope of the tangent line to the graph of f(x) at the point (–6, – 25) is The…

A: All the answers are given below

Q: 5. Evaluate sin y - dy dx y

A:

Q: 109. f(x)=x* tan x³ -x In (1+x2), then the value of (b) 1 dª f(x) dx 4 at x = 0, is: (d) 15

A:

Q: n k=1 Note: Your answer should be in terms of n.

A:

Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

A: This is a problem of vectors and integration. Based on concepts and formula of arc length we will…

Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = 1|3

A:

Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: Solve the differential equation by separable variable

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Height is given by f(t)f(t)=-16t2+420t+6t =11.5

Q: x²+2x+1 dx (x+2)(x−1)²

A:

Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

A:

Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

A:

Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

A: