Enter a math problem...
error msg
- Algebra
- Calculus
- Trigonometry
- Matrix
- Differential
- Integral
- Trigonometry
- Letters
Question
\lim _{x\rightarrow 1}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)
Evaluate the limit
\textrm{The limit does not exist}
Evaluate
\lim _{x\rightarrow 1}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)
Evaluate the left-hand and the right-hand limits
\begin{align}&\lim _{x\rightarrow 1^{-}}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)\\&\lim _{x\rightarrow 1^{+}}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)\end{align}
Evaluate the left-hand limit
More Steps
Evaluate
\lim _{x\rightarrow 1^{-}}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)
Rewrite the expression
\frac{\lim _{x\rightarrow 1^{-}}\left(e^{x}+7\right)}{\lim _{x\rightarrow 1^{-}}\left(\left(x-1\right)^{3}\right)}
Calculate
More Steps
Evaluate
\lim _{x\rightarrow 1^{-}}\left(e^{x}+7\right)
Rewrite the expression
\lim _{x\rightarrow 1^{-}}\left(e^{x}\right)+\lim _{x\rightarrow 1^{-}}\left(7\right)
Calculate
e+\lim _{x\rightarrow 1^{-}}\left(7\right)
Calculate
e+7
\frac{e+7}{\lim _{x\rightarrow 1^{-}}\left(\left(x-1\right)^{3}\right)}
Calculate
-\infty
\begin{align}&-\infty\\&\lim _{x\rightarrow 1^{+}}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)\end{align}
Evaluate the right-hand limit
More Steps
Evaluate
\lim _{x\rightarrow 1^{+}}\left(\frac{e^{x}+7}{\left(x-1\right)^{3}}\right)
Rewrite the expression
\frac{\lim _{x\rightarrow 1^{+}}\left(e^{x}+7\right)}{\lim _{x\rightarrow 1^{+}}\left(\left(x-1\right)^{3}\right)}
Calculate
More Steps
Evaluate
\lim _{x\rightarrow 1^{+}}\left(e^{x}+7\right)
Rewrite the expression
\lim _{x\rightarrow 1^{+}}\left(e^{x}\right)+\lim _{x\rightarrow 1^{+}}\left(7\right)
Calculate
e+\lim _{x\rightarrow 1^{+}}\left(7\right)
Calculate
e+7
\frac{e+7}{\lim _{x\rightarrow 1^{+}}\left(\left(x-1\right)^{3}\right)}
Calculate
+\infty
\begin{align}&-\infty\\&+\infty\end{align}
Solution
\textrm{The limit does not exist}
Show Solutions
