Find the linearization of the following functions at x=0. a) sin x L(x)= b) cos x L(x)= c) tan x L(x)= d) ex L(x)= e) In (1+x) L(x)=0 Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) = Vx, a=255.9 Set the center of the linearization as x =. Estimate the volume of material in a cylindrical shell with length 15 in., radius 9 in., and shell thickness 0.7 in. O. 0.7 in- g in Question Viewer The estimated volume of material in the shell is | ] in.3 Simplify your answer. Type an exact answer, using * as needed. Use integers or decimals for any numbers in the expression.) The concentration C in milligrams per milliliter (mg/ml) of a certain drug in a person's blood-stream t hours after a pill is swallowed is modeled by C(t) = 8 + - 4t -e-0.03. Estimate the change in concentration when t changes from 20 to 40 1 + 1 3 minutes. Answer the questions below about the function whose derivative is f'(x) = (x -4)(x+8) (x + 1)(x- 7)' , x# - 1, 7. a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? C. At what points, if any, does f assume local maximum and minimum values? Answer the following questions about the function whose derivative is given below. a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum or minimum values? f'(x) = (3 sin x - 3)(2 cos x + 1), OSXs2n3. Find the open intervals on which the function is increasing and those on which it is decreasing. b. Identify the function's local extreme values, if any. saying where they occur. g(t}= -2t2+3t+5 a. Find the open intervals on which the function is increasing and those on which it is decreasing. b. Identify the function's local extreme values. if any, saying where they occur. f(x) = 3x In x 3. Find the local extrema of the function f(x) = cos 2x + 3 sin 2x on the interval 0 s x s n, and say where they occur. b. Graph the function and its derivative together. Comment on the behavior of f in relation to the signs and values of f'. E E a. Find the local extrema of the function f(x) = sec 2x + 2 tan x on the interval E