calc 2 math problems, Exercises of Calculus

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MATH 2414 Calculus II

Final Exam

Question 1

Let be a continuous function on such that on. If the area between and the -axis on is , then find the average value of on this interval. A B C D E F

~

· 1. -

5 --^ G^13

= -^22

T

D

E

F

Question 4

The region bounded by and in quadrant I, is revolved around the -axis and a solid is generated by this revolution. Which of the following integrals represents the volume of the solid? A B C D E

Question 5

15

3: ax

X3- 9X =^0

shel method X(x2-^ 9) I air (^) = 932 πx(ax

• (^) x3) ~

Find the solution of the following differential equation given that : A B C D E F

Question 6

Evaluate the following integral: A X =^2 & (^) y =^ S Jay enly-7) :

In/8-7) enly-7) : 0 =

0 =^ St

= ~

C

D

E

F

Question 8

Find the limit of the following sequence: A B. C. D E (^). ~ In

F

Question 9

Find the sum of the following geometric series: A B C D. E F

Question 10

~ an

-^15 I:s J = -^7 Fis

T

I ~ BDT (^70) diverges

E

Question 12

Find the interval of convergence of the following power series: A B C D E

Question 13

We know that Using this information, write the first three nonzero terms of the Taylor series for centered at. ~ onon O I X= (^10) on To

[-10,^ 10]

• on YonI th

• I^ D^ =^4 P=^4 n410n (^) n 471 471

converses

converges

↓

A B C D E F

Question 14

Rewrite the algebraic equation in its equivalent polar form. A B C D 1

16 1- (^) #

5-2 +

= 5 -^ 10x^

x

~ X 2

• (^) yz 14y +^ 4/9^ =^49 X = (^) rCOSO x2 +^ y2 - 14y =^0 Yersing x & (^) + y2 =^149

x2 +y2 =^

r r2 = -^14 using

• r r =^ 14 sing

E

F None of the above.

Question 16

Find a parameterization for the line segment from. A , B , C , D , E , F

Question 17

Find a parameterization for the following elliptic curve: . A , I ~ X (^) , (^) y ,

x2y2yX =^ XI + T(x2^ -^ X^ ,^ )

Dy=^ y1 +^ T(y^

• Y1)

Ax = 3 +^ T(-^2 - 3)

AX = 3 -^ 5t

Dy =^4 +^ +(

Dy =^4

• 2t ~ 196 2COSO ,^7 Sing

B ,

C ,

D ,

E ,

F

Question 18

Find the equation of the tangent line to the curve at the point. A B C D E F ~

16- 82 X(2) =^4 +^ 2x(2)=^6 6(2) ?

y (2)^ =^10

= 6 24 - 4

y

• y1 = m(X- xi)

  = (^5)

y

• 10 =^ 5(X -^ b)

y-^10 =^ 5X-^30

10 +^10

y =^ 5x

• 20

B I want to have points deducted from my test for not working this problem.

(^986) +^2 :0 t^ : undefined It arcan (^) (

arctan (8) -

-arctan()

3X-^7 A^ +^ B (x+2)(X- 3)(x+2)(X- 3) A(X- 3) + (^) B(X+2) X= 3 3x- (^7) = A(X-3) + (^) B(X+2) 3 (3)-^7 = (^) A(O) + (^) B(5) 2 = 5B

B = 2 X=^ - 2(3)(- 2) - 7 =^ AC- 2 - 3) + (^) B(O)

• b- (^7) 5AA A B (^) 3) (a)3) 3 Inkxt^

en(x- Sixeu(ax) D :^ I:

• In(ax) (^) 11X X(nX - X

= (^) en(ax) S .

24 sinG -^ It stit13^ (

,) a= 2

• a= = 2 h^ 5 t a+ 6 = 6 /4 (^) Sini-1/ a-^ b = 2 (
• (^1) -) 44/3 (t,-) 2 +^ 4 Sing^ =^ O & I 115/ / 2 + using? I
• 2 - 2 TTIl Sino =

= 410530 360 = (^120) 120

30 240 S

8 =^22.^5

(^4 22). (^5) J Cost