所屬科目：研究所、轉學考(插大)-微積分
(a)
(b)
(c)
(d)
2. Find constants a, b, c, and d so that .
3. Solve the differential equation .tan x = secx.
4. (a) Find y'(0)if .
(b) Find y'(2)if
5. If f is a continuous function such that for all x,find an explicit formula for f(x). (10%)
6. The region bounded by y=cosx, 0≤x≤π/2； and the line y=k, 0≤k≤1, is revolved about the line y =k, generating a solid S. Determine k so that S has (a) maximum volume and (b) minimum volume. (10%)
7. Find the value of the constant C for which the integral converges. Evaluate the integral for this value of C. (10%)
9. Evaluate
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.
.tan x = secx.
.
for all x,find an explicit formula for f(x). (10%)
converges. Evaluate the integral for this value of C. (10%)