Question

$f(x) = \lim_{n\to\infty} \dfrac{\tan\pi x^2 +(x+1)^n\sin x}{x^2+(x+1)^n}\\\\Then,\:\lim_{x\to0} f(x) = ?$

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Answer 1

First of all we solve the inner limit, that is lim n → ∞, and after that we solve the limit outside.