분야
pdf2018-1 Final Solution
2018-1 Midterm Exam
2018-1 Midterm Solution
2019-1 Midterm Exam
2019-1 Midterm Solution
2019-1 Spring Final Solution
1. Determine whether the following series converges or diverges.
∞
lnlnln
(sol) Let lnlnln
Then is a continuous, positive and decreasing function on
≥.
Let lnln⇒ln
⇒lnlnln
lnln
⇒
∞
∞
lnlnln
lim
→∞
lnlnln
lim
→∞
lnln
lim
→∞
lnln
lnln
lnln
By the integral test, the series
∞
lnlnln
converges.
2. Find the interval of convergence for the series
∞
.
(sol) lim
→∞
lim
→∞
lim
→∞
⇒
⇒
∞
∞
is convergent by the alternating
series test.
∞
∞
is a divergent -series with
≤.
∴ The interval of convergence is
≤
.
3. Find the area of the surface which is obtained by rotating the
following curve around the -axis.
≤≤.
(sol) ≤≤ ⇒
∴ The area of the surface is
4. Find the area of the region which lies inside the curve cos
and outside the curve .
(sol) cos ⇒ cos
⇒
⇒
∴ The area is
cos
cos
cos
cos
sin
sin
여러 과목 판매하고 있으니 판매자료 참고 부탁드립니다.
