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For Exercises 21 and 22, consider the function f given by 5x – 2, for x...
#35,37 In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...
Is the function given by f(x) = continuous at x = 5? Why or why not? 5x+2, for x 55, 5* 5x - 18, for x>5, Choose the correct answer below. O A. The given function is continuous at x = 5 because the limit is 3. OB. The given function is continuous at x = 5 because lim f(x) does not exist. X-5 OC. The given function is not continuous at x = 5 because f(5) does not exist....
22 points possible 7/22 answered Question 14 < > ✓-4-2 +4 if << -5 Let f(2)= if x = -5 3x + 20 if 2> - 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(a) I-5 lim 2-5 lim f(x) = > Next Question 21 MacBook Air
Evaluate lim,-_-4+ g(x). 1 1 for -5< x < -4 X + 1 g(x) = 22 for X > -4 1 16 The limit does not exist. 1 3 -4
In Exercises 21-22, give the equation of the line that is the intersection of the given planes. 21. p1: 3(x-2) +(y 1)+4z 0, and p2: 2(x-1)-2(y+3) +6(2-1) 0 In Exercises 23-26, find the point of intersection between the line and the plane. 26. line: (1,2, 3) +t (3, 5,-1), plane: 3x-2y- z=-4 In Exercises 27-30, find the given distances. 27. The distance from the point (1, 2,3) to the plane 3(x-1)+(y 2)+5(2-2) 0. In Exercises 21-22, give the equation of...
Evaluate the function for the given values of x. (-5x+4, for x<-1 x) = ), 2 + 3 1, for -1 5x</ 2 for x (a) f(-1): (b) f(3)
Sketch the graph of an example of a function f that satisfies all of the given conditions. lim f(x) = 4, lim f(x) = 2, lim f(x) = 2, f(3) = 3, f(-1) = 1 x-1 x3+ X-3- у 5 у 5 3 3 -6 - 4 -2 LX 6 N 4 -6 - 4 -2 - 1 - 1 O 5 5 4 ON 3 -6 -4 . -2 2 4 6 -6 -4 -2
Find f'(x) f(x) = x х Consider the function f(x) = 5x + x Bx a. Find f'(x) b. Find the x-values where the tangent line is horizontal Use the product rule to differentiate. Do Not Simplify y = (7x4 - x + 2)(x5 + 4)
Consider the function and the value of a. f(x) = -5 X - 1 a = 3 (a) Use mtan f(a+h) - f(a) = lim to find the slope of the tangent line mtan h0 h = f'(a). = mtan 5 4 (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) »- 3 = (x – 3) x Consider the graph. у 5 x...
x if x>3 if 2<x<3 if x < 2 Given the following piecewise function: f(x)={-x |-0.5x if it exists. h Find lim f(2+h)-f(2) -0+