Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
For cos x cos 3x – sin x sin 3x = 0, use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval x (0,7). The answer is 21 22 = 23 = and 14 with xi < 22 <<3 < 24.
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. xy) =x"cos(y) +x"win(x) cos(x)sin(y). Plo The direction in which the given function txy_f(xy)-x3cos(v)+x2vsin(x) + cos(x)sin(y)increases most rapidly at P 0주 is u: " (Type exact answers, using radicals as n (xy)=x3cos(y)+x"win(x)-cos(x)sin(y) The direc on in which the given function f(xy- is eases most rapidly at (Type exact answers, using radicals as needed The derivative of the...
Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0 < x < 3
Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
Question 17 Find ALL critical numbers of f(x) = sin? x + cos, for 0 <<< a r=0, 2 = 0, 7, x = 0, 7, 2 = 0, 5, 5, 2 7T D
Question 2 Letfn:[0, 1]-R, F.(x)= n+cos(x) and f(x)= limfn(x), x € [0,1]. Find f(In(2)). ne* +sin(x)
Determine f(x).
f′′(x)=−cos(x)+sin(x), and
f(0)=1, f(π)=0.
Problem. f"(t) = -cos(T) + sin(), and f(0) = 1, f(1) = 0
F- [y - yz sin x,x + z cos x,y cos x] from OstsT/2 where the path is defined as follows x- 2t y = (1 + cost)2 z- 4(sint)3 m. F= [8xy®z, 12x2y®z, 4x2yaj from (2,0,0) to (0,2,π/2). The path is a helix of radius 2 advancing 1 unit along the positive z axis in one period of 2Tt. We were unable to transcribe this image
F- [y - yz sin x,x + z cos x,y cos x] from...