# Was this the cause of yesterday's earthquake?

Calculus Level 4

Mayank and Akul have a very strong feeling that the existence of the following expression was cause of the Afghani earthquake dated 26/10/2015

Let $$f(x)$$ = $$\sum _{ r=1 }^{ \infty }{ sec(\frac { x }{ { 2 }^{ r+1 } } ) } .\int _{ 0 }^{ \frac { x }{ { 2 }^{ r+1 } } }{ (1+{ e }^{ sint } } +{ tan }^{ -1 }t)dt.\int _{ -1 }^{ \frac { x }{ { 2 }^{ r+1 } } }{ \frac { ln(1+t) }{ t } } dt$$

for $$x\epsilon [-1,1]$$

Find the value of $$\lim _{ x\xrightarrow { } 0 }{ \frac { f(x) }{ x } }$$

If the answer can be expressed as $$\frac { { \pi }^{ a } }{ b }$$

Find the value of a+b

Remember to be very wise in your approach

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