- #1

Krushnaraj Pandya

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## Homework Statement

if f(x)= lim(n→∞) e^(xtan(1/n)log(1/n)) and ∫f(x)/(sin^11x.cosx)^1/3 dx=g(x)+c, then

1) g(pi/4)=3/2

2) g(x) is continuous for all x

3) g(pi/4)= -15/8

4) g(pi/4)=12

**2. The attempt at a solution**

Part a-Evaluating the limit, since 1/n tends to 0, log(1/n)→-∞=-n, using tan(1/n)/(1/n)=1, I get f(x)=e^(-x)

Part b-I tried substituting -x=t, which gives -∫e^t/(-sin^11t.cost)...I'm stuck here, would appreciate some insight, also let me know if part a is correct (I'm not very confident)