Unformatted text preview: 6. (15 pts)
Let V01) be the volume obtained by rotating the region bounded by the coordinate axes,
1 the line .1? = a + at2 and the curve y : x/H—ﬁ around the line a: = "1.
a: (a) Give a formula for V01). (Do not try to evaluate the integrall) (b) Evaluate %' (c) Is there a value of a > 0 for which V01) 2 a? Explain your answer.
7. (10 pts) (a) Find an equation for the line tangent to the curve 51:3 + y4 = 2 at (1, 1).
(b) Let R be determined by the equation 1-1+: R ‘ R1 R2 If R: is decreasing at the rate 1 and R2 is increasing at the rate 0.5, at what rate is
R changing when R1 = 75 and R2 = 50? 8. (25 pts)
Evaluate the following integrals (a) / Einstein:
(d) j (1 + $)2(1 + $2) (e) f% xda:
o v 1 — 3:4
9. (10 pts)
Let f (as) = [0 tan tdt. Compute the length of the graph of f over the interval [0,1r/4]. 10. (15pts)
Find the following limits if they exist
(a) lim (In :17)” a” (b) lim (ex + $2)(e'w + 1M) (c) lim f6“ sintdt LE—+0+ 1712 ...
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- Fall '07