2. Integrals containing sin u cos v can be solve using identity. (a) Double-angle (b) Half-angle (c) Product to Sum (d) Sum to Product

Q: dx x* + 4

A:

Q: y = (sinh(@)) Solve for y'. Express your answer by factoring out a common facto

A: First I have taken the log on both side to the given function and then differentiating it with…

Q: For the given function find dy/dx. = x +2

A:

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: Question 4 Given the expression below, +. 4rab determine y". Upload Choose a File

A:

Q: Evaluate the following definite integrals. 3. If f(x) = V19+f dt ,find f'(3).

A: We can solve as follows

Q: Given: y = arctan sinh find y' at x = 2 cosh 1 1+sinh 1 cosh 1 %3D 3(1+sinh 1) cosh 1 1+sinh 1 cosh…

A:

Q: r2 lim cos where k is - 00 - sec?! (A lim tan B lim - cos?- lim 2. 2.

A:

Q: Ir(t) - u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A:

Q: Question 3 Determine the derivative of In(csc x) cot x Csc I - cot x CS z Previous

A: A detailed solution is given below

Q: Use substitution to find the indefinite integral. Зх + 7 (6x + 28x) 5 3x +7 (6x² + 28x) =xp.

A:

Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

A:

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Find the second derivative (y") of the given function: 6. 2-e

A:

Q: (-x+82.762) 1(x) = 0.5e - 25.7 12 М m(x) — 0.15(х - 90)2 — 25.7

A: To find thee first and second derivative of the functions given.

Q: (b) Using the Power Rule for differentiation, find the derivatives for the following functions: (i)…

A:

Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

Q: Find V (V × F), if F(r, y, z) = 7e"i+6xe"j – 2ev²k. V· (V × F) =|0

A: We have to find ∇.∇×F→

Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

A:

Q: For the given function find dy/dx. = x + 2 %3D O y = 1-y-3x2-4x %3D 3y2 +2+2 O y = 1-a+3y-4x 322-y+2…

A: We know Implicit differentiation of ax+by=c is given by, a+bdydx=0 ddx(xn)=nxn-1 , for any real…

Q: about the line, x- | (E'1) puo (!!)'(0) squiad %3D V= T RG) 3-X y= 2x+1 Idy 3 - 23. x- V= T 29 12

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: A detailed solution is given below

Q: Determine whether z is a function of x and y + z2 = 1

A: see below the answer and explanation

Q: Suppose the revenue function for a product is given by the function: : R(g) = - 8g° + 4g where q is…

A:

Q: Find the second derivative of the function x2y – 2 = 5x + y

A:

Q: an +1 an +1 an + 1 Recall the Ratio Test which states that, if is a series with nonzero terms, and…

A:

Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e…

A: We know that derivatives of  d(xn)/dx = nxn-1. And d(ex)/dx = ex.   Here i attached the solution of…

Q: 3 Evaluate the following indefinite integral: 1.) f 10ma dx

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Sh dx

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Find curl (4z i+ 5x j+ 9y k). curl (4z i + 5x j + 9y k) = ( Di + ( j + ( i i )k

A:

Q: Question 3 Find the first derivative of the function below: f(x) = (cos(2z -7))sin(z+1) Upload…

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 6 cos(t)i +6 sin(t)j+…

A: As we know that; The expression for the curvature; κ=r't×r''tr't3 And The expression for the radius…

Q: N h(x) = -0.8(x + 5)+39.9482 i(x) = 2-0.8(x-43.79)

A: 7) h(x)=-0.8(x+5)+39.9482 8)i(x)=2-0.8(x-43.79) 9) j(x)=0.1(x-57.5)2-0.0025(x-57.5).

Q: Fill In The Blank Refer to the given below. Find the indefinite integral. Simplify your final…

A:

Q: Question 2 Differentiate the following function without simplifying y = arc sec(sec(02)) You may use…

A:

Q: Find div F and curl F if F(r, y, z) = 13y"2°i – 11a2°j – 7xy°k. div F= curl F=

A: We have to find the  divF and curl F

Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

A:

Q: Sketch the region whose area is given by the definite integral. 8. x dx

A:

Q: What is the absolute maximum and absolute minimum of the function f(x) = x3 – 3x2 – 9x – 6 in [0,5]?

A:

Q: (2.x+ 5y)dx + (4.x – 5y)dy =

A:

Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: dy onsider the differential equation dx y? ) Re-write the equation in terms of differentials: dy =…

A: Given query is to find the solution of the differential equation.

Q: Determine the vector field of F. F(r, y) = yi – xj

A:

Q: Determine wnetner the function Isa linear transrormation. T: R2 - R³, T(x, y) = (x², 3xy, 2y²)…

A:

Q: S- 3 dy 3y - sin –+C 4– 9y2 3 A True B) False ||

A:

Q: xe - ye" = In(xy). Find dy/dx.

A:

Q: Use the function to find the image of v and the preimage of w. T(V,, V2) V2, 2v, v= (7, 7), w =…

A: In given problem we have to find the image of given vector 'v' and preimage of given vector 'w' .

Q: dx (х -1)3

A:

Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y² + z2 subject…

A: