## Related questions with answers

Question

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. $\lim _{x \rightarrow 0} \frac{x}{e^{x}}=1$

Solution

VerifiedStep 1

1 of 2$\displaystyle \lim_{x\to 0}\dfrac{x}{e^x}\\$

If x is close to 0,$e^x$is close to 1, so the ratio is close to zero

Hence$\displaystyle \lim_{x\to 0}$\dfrac{x}{e^x}$=0\neq 1$

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