7 6 (A) -33 (B) -27 (C) 27 (D) 33 6. What is most nearly the volume of the objec

Question

7 6

(A) -33
(B) -27
(C) 27
(D) 33

6. What is most nearly the volume of the object cre- ated when the area bounded by y·0, 0, and -v4- is rotated about the I-axis? (A) 3.1 (B) 8.4 (C) 17 (D) 34 7. Simplify the following expression: x2-16 lim (A) 0 (B) 8 (C) 12 (D) 16 8. Find the area under the curvey-lk between the limits j-2 andy-10 (A) 1.61 (B) 2.39 (C) 3.71 (D) 3.97 9. What are the roots of the cubic equation r-8r-3-0? Hint guess one rootfirsit. (A) x=-7.90,-3,-0.38 (B) -3-22 (C)3,-0.38, 2 (D) -2.62, -0.38, 3 10. What is the determinant of the following 2x2 matrix?

Explanation / Answer

6)y=sqrt(4-x^2) ==>y^2 =4-x^2==>x^2=4-y^2==>x=sqrt(4-y^2)

sqrt(4-y^2)=0==>4-y^2 =0 ==>y^2 =4 ==>y=2

volume =pi *integral[0 to 2](sqrt(4-y^2))^2 dy

=pi *integral[0 to 2](4-y^2) dy

=pi *[0 to 2] 4y-(1/3)y^3 +c

=pi * [4*2-(1/3)*2^3 +c -0+0-c]

=16.76

7)limx->4 (x2-16)/(x-4)

limx->4 (x-4)(x+4)/(x-4)

limx->4 (x+4)

=4+4

=8

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