Friday, March 23, 2018

calculus - What is limlimitskto0f(k)=2+kfrac32cosfrac1k2

Just want to check this one:



I got:



lim



Since \lim\limits_{k \to 0}\cos{\frac{1}{k^2}} = 0, using the squeeze theorem, I have \lim\limits_{k \to 0} k^{\frac{3}{2}}\cos{\frac{1}{k^2}} = 0.



So
\begin{align*} \lim_{k \to 0}f(k) &= 2 + \lim_{k \to 0}k^{\frac{3}{2}}\cos\left(\frac{1}{k^2}\right)\\ &= 2 + 0\\ &= 2 \end{align*}



Is this correct?



Thanks!

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