key with work IBP Integration by Parts Name Signature:

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1 Math 128 Exam #1 Fall 2017 SPECIAL CODE: key with work IBP Name Signature: Integration by Parts ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Academic Honesty Statement: By signing my name above, I acknowledge that I understand each of the following behaviors: using a calculator or cell phone (or any other communication technology); referring to a piece of paper or object with helpful information on it (cheat sheet, notes, etc); looking at a test or answer sheet that is not my own; allowing another student to look at my test or answer sheet; communicating with other students (verbally or nonverbally); taking the test for another student; taking my bubble sheet of answers with me when I've finished; talking while waiting to hand in my test materials to the proctors; sharing a calculator to be a form of academic dishonesty (cheating) I am also pledging not to engage in any of these behaviors I understand that if I do engage in these behaviors, the consequences will be failure of the exam and a formal charge of academic dishonesty to the Ombuds Office ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Please shut off all cell phones, ear phones, computers, beepers, smart watches, etc Please put everything away except a #2 pencil and a calculator that is NOT your cell phone You may write on the test There are twenty five multiple choice questions and each question is worth four points 1 On the bubble sheet, where it says Name, please print your last name, leave a space, and then print your first name in the rectangles Then fill in the bubbles underneath 2 On the bubble sheet, where it says Identification Number, please write your entire Student ID number in the rectangles and fill in the bubbles underneath Please double check to make sure you bubbled in your ID # correctly 4 On the bubble sheet, where it says Special Codes, please write the numbers: in the rectangles and fill in the bubbles underneath Please double check to make sure you bubbled in the special code correctly Please make sure you bubble in your answers carefully on the bubble sheet and circle your answers on your test booklet

2 Formulas: PV M 0 S(t)e rt dt FV PVe rm b P (t) dt ln (P(b) P(t) P(a) ) a udv uv vdu IBP

3 1) Consider the graph of f(x) below: Which of the following is the largest? (A) e f (x)dx a + I + but smaller than (B) b (B O) f (x)dx a A and clearly larger than (D) (C) (D) c f (x)dx b e f (x)dx c A 2) A bacteria colony initially has a population of 8 million Suppose that the population is growing at rate of f(t) 2 t million bacteria per hour What is the best approximation of the population, in millions, after 3 hours? 3 calculator (A) 1734 (B) (C) 1810 to changeover (D) t So Idt w I 0,33 Integral of the Rate of Change

4 c' Cct 3) Consider the graph of f (x) below: ', Suppose f(0) 2 What is the value of f(2)? (A) 1 O (B) 05 (C) 4 (D) 1 flat fgoytffi# fi ( 32) 4) A company determines that its marginal revenue (in dollars per day) is given by R (t) 150e t The company s marginal cost is given by C (t) t (in dollars per day) Find the total profit over the first five days (from t 0 to t 5) 6(A) $21,516 Profit (B) $21,667 (C) $21,508 PHI Rct ) Revenue ) Cost P'HR' At 150 et (D) $21,519 ( P' HI R' HI c' m in at in HI ;Iit% f?: T poet '3t fo5i5oet It ) EEE EEE ' : So5P'Hdt ) rahfeffohange of profit laoto3tdtaca#or2h5t5tv

5 X 9) 5) The rate that ice is forming on a pond is modeled by F (t), measured in inches per hour and t is measured in hours since 9AM What does the following integral represent? (A) There is not enough information 2 F (t)dt 0 (C) At 11AM, the pond has 34 inches of ice D 34 (B) Between 9AM and 11AM, 34 inches of ice formed (D) Between 9AM and 11AM, ice formed at a rate of 34 inches per hour f Zhrs HAM F' Htdt AMOUNT OF ICE FORMED to hrs 9AM Orahteofohange between 9AM I to ) and HAMAS ) of ice formation 3,4 6) What is the area enclosed by the curves y x 2 2x and y x? (A) 9 (B) 4 3 intersection : X ' 2x x' 3*0 XCX 370 X 0,3 (C) 5 3 (D) 9 2 i iia: ::: 53 7! ( Hz Co o )

6 ' 7) Find the average value of the function f(x) 3 on [4,9] x (A) 6 (B) 7 (C) 76 avg Iota S! find x (D) 12 g S! 3 x O E I! Ix E La ' 4 IS! x 7 Ix Eg ( 3 2) I ) A firm s profit function is modeled by P(x) 1 dollars, where x is the number of units 1+x sold What is the average profit for the first 50 units sold? (A) ln(51) dollars O 50 over o (B) ln(26) 50 dollars (C) 26 dollars (D) 51 dollars avg to sod too S! ttxdx In I I txt to 50 to [ In 15h In lip To [ In 151 ) o ] lh'd

7 9) Suppose the demand function is D(q) q 2 + q + 5 and the supply function is S(q) q 2 q + 1, at what price and quantity is the market in equilibrium? (A) p 8, q 3 (B) p 44, q 2 Did intersects she ) at pit) (C) p 16, q 2 (D) p 3, q ) 219 2) Gti )0 't p sand? p Dl9* ) p slg*) 3 3 Dta or/9* :ET o must be I 10) Suppose the demand function is DDP0 given by D(q) 100 4q What is the consumer surplus when the equilibrium quantity is q 10? (A) 175 (9913*7110,60) (B) 200 Ap ~ W (C) egalitarian Pt Dlg ) Goddamned (D) ' Consumer surplus areal KEY L

8 P 11) Find the producer surplus when the market is in equilibrium if the supply function is given by S(q) q 2 + 4q + 7 and the demand function is given by D(q) 82 6q (A) 127 (B) 75 equiloriun : SH ) Dlg ) Gg 9710g 750 (C) 335 (D) Est 't Dlg ) 't ' P No! I ' :O:*: Isa said is: i', * Igt I 5) (95) dg canyon Inanity,, font 333 ( Eg ) 12) Suppose a company is expected to earn $500 per year, at a continuous rate, over the next ten years with a continuous interest rate of 4% The rights to the earnings are the company are for sale now for $5,000 Is it advised to buy the earning rights to this company? (A) Yes, purchase the company for $5,000 because it will earn $6148 over ten years (B) No, do not purchase the company for $5,000 because it will earn less than $5,000 over ten years (C) Yes, purchase the company for $5,000 because it will earn $7459 over ten years O (D) No, do not purchase the company for $5,000 because it is worth $4121 today any : compute the PV of the $5001 yr continuous payments : pv Siosoo e tdtee#r$4i2i So the company is only worth $4,121 TODAY, SO you should not purchase it for $513

9 13) Consider the table below: Population of California (in millions) Year Population What is the relative increase between 2006 and 2007? (A) 5% 9(B) 53% relative PC2007)Pl2oo# (C) 61% (D) 59% increase 396 PC 2006 ) 376 3, 0, ) If the monthly mortgage payment for a home that cost $116,500 is $83333 with an interest rate of 6% compounded continuously, what is the length of the loan? (A) Between 12 and 18 years of loan in YEARS (B) Between 19 and 24 years (C) Between 25 and 30 years (D) Between 31 and 36 years Find M length e ' 6tdt prgg#rtdtds12x83333/moyfh or nosfmeaott ( e e )ti m In ( 1165 ( 006 ) TI ) 2001 years

10 15) The relative rate of change of a population of fish is modeled by P (t) 8t 25 P(t) 9t+7 By what percent did the population change over from t 0 to t 10 years? (A) Increases by 79% (B) Decreases by 23% (C) Increases by 21% (D) Decreases by21% in S! PIET at So HITTITE :* o 231 e In lpf ) a O Ppi e e 923 ' 231 page I e 923 ' pay Plo ) w decrease by 2021 or I ) Evaluate the integral below: ( x + 1 x4) dx (A) 2x 3/2 1 5x 5 + C O (B) 2 3 x3/2 1 + C 3x 3 (C) 2 3 x3/2 1 5x 5 + C (D) 2x 3/2 1 3x 3 + C S x' t I dx II t Esto 23,

11 aetytycos 17) What is the antiderivative of f(t) 1 t 2et + sin ( t 4 )? (A) ln t 2e t 1 4 cos (t 4 ) + C (B) (C) (D) ln(t) 2e t 1 4 cos ( t 4 ) + C 1 t 2 2et 4cos ( t 4 ) + C ln t 2e t 4cos ( t 4 ) + C FAI InlH ffcttdt ff 2ettsinHt)dt # Htc flnhi2et4coshht 18) Evaluate the integral below: x 3 x dx ScxH43dx (A) O 1 6 (x4 + 7) 3/2 + C wx4t7 fw' (B) 2 3 (x4 + 7) 3/2 + C (C) 1 2 (x4 + 7) 1/2 + C dw4pdx tydw dwidxzwtt # YatC (D) 1 4 x4 2 3 (x4 + 7) 3/2 + C ECx4t7)

12 19) Evaluate the integral below (A) 5 3 x x 2 + C (B) 10x 3x 4 + C O (C) 5 3 x3 1 2 x 2 + C (D) 5 3 x x 2 + C (5x 2 + x 3 )dx 5 tiitc Fx' xa 20) Find f(x) with initial conditions given below: (A) f(x) cos(7x 2 + 3x) 6 O (B) f(x) cos(7x 2 + 3x) 4 (C) f(x) cos(7x 2 + 3x) 5 (D) f(x) cos(7x 2 + 3x) 5 f (x) (14x + 3) sin(7x 2 + 3x) with f(0) 5 fix, _ Sftxldx upto a constant SsinfxIzx)Hdx w dw w7x73x due )dx fsinwdw C? /fmcosgx73x) 5fH It cos cosw 6) t C Dci

13 Sadr ur 21) Evaluate the integral below: IBP x 3 ln(4x)dx x4lnhx) (A) 1 4 x4 1 2 (ln(4x))2 + C ulnc4x ) v 4x4 Svdu ftyxxdx (B) 1 4 x4 ln(4x) 1 16 x4 + C da du O _ 4dx x' dx (C) 1 4 x4 ln(4x) 1 4 x4 + C (D) 1 4 x4 ln(4x) x5 + C * 4W4x) tyfxdx fx4hc4xtfx# 22) When trying to evaluate the integral below using usubstitution, which of the following would be the resulting integral? x 2 (x 3 3) 16 dx (A) You cannot use the method of u substitution to evaluate this integral (B) 1 3 u2 (u 3) 16 du O (C) 1 3 u16 du (D) 3 (u 3 3) 16 du Six 's '5x2dx IT Sdu a x' 3 tzduxdxfssuam _3x2dx fu ' ' Ida

14 IBP 23) Evaluate the integral below: (x 2 + 2x)e 3x dx (A) 1 3 (x2 + 2x)e 3x 1 9 (2x + 2)e3x e3x + C (B) 1 3 (x2 + 2x)e 3x 1 (2x + 9 2)e3x 2 27 e3x + C (C) 1 3 (x2 + 2x)e 3x 1 (2x + 9 2)e3x e3x + C 1st IBP : TWICE! KIT ux7zx practice! du _e3 d (D) 1 3 (x2 + 2x)e 3x 2 3 (2x + 2)e3x 2 3 e3x + C ± 24) Evaluate the integral below: (A) 1 e 14 (B) 1 1 e14 (C) 0 (D) 1 off 14 14e 14x 1 dx sie mx#i4y;msiehdxj, eµ dxhisn egoestoo E ie I it [ o ] ee

15 25) Use the Fundamental Theorem of Calculus to find the area under f(x) x 2 from x 1 to x 2 (A) 9 7 (B) 7 3 (C) 3 (D) 4 i area Sixth, Ix ' 1,2 I (2313)1}J