1.Evaluate the integral ∫tan-1(4t)dt
2.Evaluate the integral ∫e^√x dx
3.Evaluate the integral ∫(1/3sinθ-4cosθ)dθ
π/2
4.Evaluate the integral ∫ (cost/√(1+sin^2t))dt
0
5.Determine whether the improper integral diverges or cinverges. Give reasons
for your answer.
1
∫(e^x/(e^x-1))dx
-1
6.Determine whether the sequence converges or diverges .If it coverges,find
the limit.
a =(1+2/n)^(1/n)
n
7.Find the sum of the series.
∞
Σ(1/((4n+1)(4n-3))
n=1
8.Find the values of P for which the series is convergent.
∞
Σ (㏑n/n^p)
n=2
9.Determine whether the series converges conditionally or absolutely, or
diverges.
∞
Σ(-1)^n sin(π/n)
n=1
10.Find the radius of converhence of the power series.
∞
Σ ((n!)^3/(3n)!)x^n
n=0
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