Question

im stuck at this question. how to evaluate lim┬(x→∞)⁡〖(cos⁡(2/x))^(x^2 ) 〗

Answer 1

\[\large \lim_{x \rightarrow \infty} [\cos(\frac{ 2 }{ x })]^{x^2}\]

Answer 2

maybe try a natural log to move the exponent...e^ln(x) = x


\[\large \lim_{x \rightarrow \infty} [e ^{\ln(\cos(2/x)^{x^2}}]\]
\[\large \lim_{x \rightarrow \infty} [e ^{x^2*\ln(\cos(2/x)}]\]

Answer 3

here is the sorry. oops it is e^(-2).

Answer 4

@Miaaziz

Answer 5

thank you @DanJS . thank you @jango_IN_DTOWN