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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Evaluate the limit from the right side as $x$ approaches $-6$

step 2

The expression $\frac{e^{2x}}{x+6}$ becomes undefined as $x$ approaches $-6$ from the right, since the denominator approaches $0$

step 3

As $x$ gets closer to $-6$ from the right, $e^{2x}$ approaches $e^{-12}$, which is a positive constant

step 4

Since the numerator remains positive and the denominator approaches $0$ from the positive side, the limit tends to $+\infty$

Answer

$\lim _{x \rightarrow -6^{+}} \frac{e^{2 x}}{x+6} = +\infty$

Key Concept

Limits involving a non-zero constant divided by an expression approaching zero

Explanation

As $x$ approaches $-6$ from the right, the denominator of the fraction $\frac{e^{2x}}{x+6}$ approaches zero, causing the value of the fraction to increase without bound. Hence, the limit is $+\infty$.

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