Find the limit of (e^x^2-1)/cos(x-1) as x approaches 0

 Exercise

$\lim_{x\to0}\left(\frac{e^{x^2}-1}{cos\left(x-1\right)}\right)$

 

Evaluate the limit $\lim_{x\to0}\left(\frac{e^{\left(x^2\right)}-1}{\cos\left(x-1\right)}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{e^{\left(0^2\right)}-1}{\cos\left(0-1\right)}$

 

Subtract the values $0$ and $-1$

$\frac{e^{\left(0^2\right)}-1}{\cos\left(-1\right)}$

 

Calculate the power $0^2$

$\frac{1-1}{\cos\left(-1\right)}$

 

Subtract the values $1$ and $-1$

$\frac{0}{\cos\left(-1\right)}$

 

Zero divided by anything is equal to zero

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