Calculus 1 Problem Sets (Limits, Derivatives, Definite Integral....)

Posted Under: Calculus

Ask A Question

Hire Experts For Answers

Order Now

Related Study Services

DESCRIPTION
Posted
Modified
Viewed 19
I need all questions answered with a step by step process of how you got it (show work). It can be handwritten and sent to me by pictures.

This order does not have tags, yet.

Attachments
Name: Date: Calculus Problem Set 5 Fall 2021 For problems 1 – 20, write the letter of your answer in the space provided. 1. = Answer: __________ a) -10 b) -1 c) -2 d) 2 2. = a) -1 b) Does not exist c) d) Answer: __________ 3. = a) b) Does not exist c) 0 d) Answer: __________ 4. find a) 2 b) Does not exist c) 1 d) Answer: __________ 5. a) 0 b) Does not exist c) 1 d) Answer: __________ For problems 6 – 11, find the derivative of the function. 6. f(x) = , f '(x) = Answer: _________ a) b) c) d) 7. f(x) = , f '( x) = Answer: __________ a) b) c) d) 8. f(x) = 6xcos(x2), f '( x) = Answer: __________ a) -12xsinx2 b) 6cos(x2) – 12x2sin(x2) c) 6cos(x2) + 12x2sin(x2) d) 12xsinx2 9. f(x) = arcsin3x, Answer: __________ a) b) c) d) 3cos3x 10. f(x) = , f '(x) = Answer: __________ a) b) -2x c) ln(-x2) d) -2x ln(-x2) 11. , f '(x) = Answer: __________ a) b) c) d) 12. For what values of x is the function f given by f(x) = x3 – 12x + 24 increasing and/or decreasing? a) increasing, decreasing (-2, 2), increasing (2, ) b) decreasing , increasing (0, ) c) increasing d) decreasing e) decreasing, increasing (-2, 2), decreasing (2, ) Answer: ________ 13. For f(x) = which of the following statements is not true? a) f(x) has a relative maximum at x = 1 b) f(x) is increasing for c) f(x) is concave up for d) f(x) has a point of inflection at x = 2 e) f(x) has a relative minimum at x = 3 Answer: __________ 14. For what values of x is the graph of y = x3 – 3x +2 concave upward? a) > 0 b) x < -2 c) -2 < x < -1 d) -1< x < 0 e) all values of x Answer: __________ 15. Given f(x) = on the closed interval [-4, 4], what are the absolute extrema of the function? a) Min: (-4, ) b) Min: (0, 0) c) Min: (-2, ) d) Min: (-3, ) Max: (4, ) Max: (1, ) Max: (2, ) Max: (3, ) Answer: __________ For problems 16 – 18 find each indefinite integral. 16. a) 3x + + C b) 3x + C c) d) Answer: __________ 17. a) b) c) d) 6x2 + 7x – 5 + C Answer: __________ 18. a) 7x + cosx + C b) 7x + tanx + C c) 7x – sinx2 + C d) 7x – cosx + C Answer: __________ For problems 19 & 20, evaluate the definite integral. 19. a) 12 b) 18 c ) 22 d) -12 Answer: __________ 20. a) 0 b) 2 c) -2 d) Answer: __________ Directions for 21 – 30: Please do the following problems. Show all work where necessary. 21. Use the graph below to answer each question. This is not a multiple choice question. A) B) C) D) At what values of x is the function discontinuous? 22. Given y = , find dy. 23. f(x) = , f '(x) = 24. If find y' 25. 26. 27. Find the equation of the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point (1, 3). 28. For an object whose position at time t (in seconds) is given by meters, find its acceleration at t = 2 sec. 29. Find the length and width of a rectangle that has a perimeter of 56 meters and a maximum area. 30. Air is being pumped into a spherical balloon at the rate of 20 cubic feet per minute. At what rate is the radius of the balloon changing when the radius is 3 feet? Note that the volume of the sphere is given by V = . ( ) 2 38 xx +- x 5 - C x x x + - 3 3 ) 5 ( 3 C x x x + - 3 3 3 ) 5 ( ò + - dx x x ) 5 3 )( 1 2 ( ( ) C x x x x + ÷ ø ö ç è æ + - 5 2 3 2 2 C x + + 7 12 C x x x + - + 5 2 7 2 2 3 ò + dx x ) sin 7 ( ( ) ò - - 2 1 3 2 4 dt t t ò - 2 2 cos p p xdx 2 lim x ® 1 2 5 2 + x x 22 3620, yxyx +-+= ò - + dx x x ) 1 2 9 ( 2 32 ()3810 sttt =-+ 3 3 4 r p 2 2 6 4 xx x +- - 5 4 2 3 lim x ®¥ 3 3 356 248 xx xx ++ -+ 3 2 4 3 { 2 1 () 43 x fx x + = - if if < 1 1 x x ³ ). ( lim 1 x f x - ® 3 2 7 1 2 2 3 + - + x x x x x x 2 1 2 3 1 3 2 - + 3 3 2 2 2 3 1 x x x - + 3 3 2 2 2 3 1 x x x + + 3 3 2 2 2 3 1 x x x + + ( ) 4 2 43 x - ( ) 3 2 3243 xx - ( ) 3 2 43 x - ( ) 3 2 443 x - ( ) 3 48 x = ) ( ' x f 2 x e - 2 x e - ) 9 ln( ) ( 2 - = x x f 9 2 2 - x x 9 1 2 - x 9 2 - x x 2 ( ) ,2 -¥- ¥ ( ) ,0 -¥ 2 lim x ®- (,) -¥¥ (,) -¥¥ 32 69 xxx -+ 1 x £ 2 x £ x ò - dx x x 2 2 5 3 x 5
Explanations and Answers 0

No answers posted

Post your Answer - free or at a fee

Login to your tutor account to post an answer

Posting a free answer earns you +20 points.

Login

NB: Post a homework question for free and get answers - free or paid homework help.

Get answers to: Calculus 1 Problem Sets (Limits, Derivatives, Definite Integral....) or similar questions only at Tutlance.

Related Questions