Solution: Given the following values:
Calculating:
Using the product rule of differentiation, we'll get:
Substituting x = 1, we'll get:
Substituting the given value, we'll get:
Calculating:
Using the quotient rule of differentiation, we'll get:
Substituting x = 1, we'll get:
Substituting the given value, we'll get:
I hope it helps you!
3. (10 points) Given that f(1) = 5, f'(1) = 4, 9(1) = 2, and g'(1)...
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
Suppose that f(2) = -3, 9(2) = 4, f'(2) = -5, and g(2) = 1. Find h'(2). (a) h(x) = 3f(x) - 2g(x) h'(2) h(x) = f(x)g(x) (b) h'(2) (c) h(x) = f(x) g(x) h'(2) (d) h(x) g(x) 1 + f(x) h'(2)
5 Consider the functions f and g whose graphs are given below. z y = f(x) -4 A3 -2 -1 1 2 3 4 y = 9(2) -4 -3 -2 -1 1 2 3 4 1 + f. Find (3) a. Find f'(-3). b. Find f'(1). g. Suppose p(x) = f(x)g(2). Find p'(-3). c. Find f'(3). h. Suppose q(z) = 5(). Find g(3). d. Find t'(-3). g(2) e. Find g'(1). i. Suppose r(x) = x2 f(x). Find r'(1).
0.09/1 points Previous Answers SCalcET8 5.3.002. Let g(x)-f(t) dt, where f is the function whose graph is shown (a) Evaluate g(x) for x 0, 1, 2, 3, 4, 5, and 6 g(0)0 9(2)-8 g(3)-( 20 9(4)- 9(5) 9(6) ) g(6)- (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimum x= maximum x= (d) Sketch a rough graph of g. 7 83 gtx ry again....
g(x)dx = 5, find the following Problem 4 (12 points). Given ( g(x)dx = 10 and integrals: (a) [(39(x) + 5x)dx (b) ["o() der
4. (10 points) Define g(3) in a way that extends g(x) = (x2 - 9)/(x – 3) to be continuous at x=3. 5. (10 points) If f(x) = (x -8)(1/2) , L = 5, c = 33, and epsilon = 1, find what delta has to be. 6. (10 points) Use the addition formulas to confirm if sin (ft/2 - x) = cos x is an identity. 7. (10 points) What is average rate of change of f(x) = x3...
|| -2 -1 / 1 2 3 4 5 | Graph of f (53) is that the port (335) is therhoff at the point (5,3). It is known that the point (3,3 - V5) is on the graph of a) f (x) dx = 7, find the value of 7 ()dz. Show the work that leads to your answer. Upload files (PDF, JPG, GIF, PNG, TXT, Word, Excel, Powerpoint file formats supported) 0/2 File Limit b) Evaluate (25" (2) +...
Question 2 f'(x) glx) g(x) g'(x) x 5 6 4 z 3 z -4 3 -2 2 4 5 o -5 8 2 A. find h'll), where h(x)=2x-3f(x) 3 0 a B find hils), where h(x) = f(x) g(x) C. find h (3), where h(x) = f(g(x)) D. find n (4), where h(x)= (g(x))*
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)