1. ## continuity

Use continuity to evaluate the limit.

2. Originally Posted by ryan18
Use continuity to evaluate the limit.

I'm not sure what you mean per se, but I can show that this function is continuous at $x=1$
Let $$f(x)=e^{2x^5-2x}$$.

1. $f(x)$ is defined at $x=1$

2. $\lim_{x\to1}f(x)\mbox{ exists }$

3. $\lim_{x\to1}f(x)=f(1)$.

$\therefore~{f(x)}$ is continiuous at $x=1$ by definition.

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3. Originally Posted by ryan18
Use continuity to evaluate the limit.
You said "use continuity to evaluate the limit" so I suspect you are not required to prove this is continuous. A function is defined to be continuous at x= a if $\lim_{x\to a} f(x)= f(a)$. Sinmce this function is continuous, to evaluate the limit, you just have to evaluate the function itself: set x= 1.