Limits of Exponential Functions Calculator

Solved example of limits of exponential functions

Insert an $1$ multiplying the exponent

Rewrite the $1$ as a division of $3$$\sin(x)$

Multiply the $3$$\sin(x)$ in the exponent

Rewriting the exponent

Apply the power rule of limits: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$

Applying the Sandwich Theorem, which states that: Let $I$ be an interval that contains the point $c$, and let $f(x)$, $g(x)$, and $h(x)$ be functions defined on $I$. If for every $x$ not equal to $c$ in the interval $I$ we have $g(x)\leq f(x)\leq h(x)$ and also suppose that: $\displaystyle\lim_{x\to c}{g(x)}=\lim_{x\to c}{h(x)}=L$, then: $\displaystyle\lim_{x\to c}{f(x)}=L$

Apply the limit rule of: $\displaystyle\lim_{x\to0}\left(1+x\right)^\frac{1}{x}=e$, where the $x$ represents the function $3\sin\left(x\right)$