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Evaluate the limit, using L’Hôpital’s rule if necessary. (If you need to use or , enter INFINITY or -INFINITY, respectively.)

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Mar 31,2025

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LARCALCET7 5.6.038.
ASK YOUR TEACHER
PRACTICE

Evaluate the limit, using L’Hôpital’s rule if necessary. (If you need to use or , enter INFINITY or -INFINITY, respectively.)

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Watch it
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LARCALCET7 5.6.048.MI.SA.

Ask by Washington Rogers. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

Calculate the limit $$ \lim_{x\rightarrow \infty} \frac{e^{5x-9}}{8x} $$.
Evaluate the limit by following steps:
- step0: Evaluate using L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{e^{5x-9}}{8x}\right)$$
- step1: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{d}{dx}\left(e^{5x-9}\right)}{\frac{d}{dx}\left(8x\right)}\right)$$
- step2: Find the derivative:
  $$\lim _{x\rightarrow +\infty}\left(\frac{5e^{5x-9}}{8}\right)$$
- step3: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow +\infty}\left(5e^{5x-9}\right)}{8}$$
- step4: Calculate:
  $$\frac{+\infty}{8}$$
- step5: Divide the terms:
  $$+\infty$$
The limit of $$ \frac{e^{5x-9}}{8x} $$ as $$ x $$ approaches infinity is $$ +\infty $$.
The limit is $$ +\infty $$.

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