Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used. (a) nth-Term Test (b) Geometric Series Test (c) p-Series Test (d) Telescoping Series Test (e) Integral Test (f) Direct Comparison Test (g) Limit Comparison Test ∑ n = 1 ∞ n ( n 2 + 1 ) 2
Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used. (a) nth-Term Test (b) Geometric Series Test (c) p-Series Test (d) Telescoping Series Test (e) Integral Test (f) Direct Comparison Test (g) Limit Comparison Test ∑ n = 1 ∞ n ( n 2 + 1 ) 2
Solution Summary: The author explains that the given series converges by the use of the integral test.
Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used.
(a) nth-Term Test
(b) Geometric Series Test
(c) p-Series Test
(d) Telescoping Series Test
(e) Integral Test
(f) Direct Comparison Test
(g) Limit Comparison Test
∑
n
=
1
∞
n
(
n
2
+
1
)
2
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
4. Use cylindrical shells to find the volume of the solid generated when the
region enclosed by the given curves is revolved about the x-axis.
y = √√x, y = 0, y = √√3
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