What is the limit as x approaches infinity of ((x+7)/(x+3))^{2x} ?

The limit as x approaches infinity of ((x+7)/(x+3))^{2x} is e^8

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limit as x approaches infinity of ((x+7)/(x+3))^{2x}

x \to \infty lim ((\frac{x + 7}{x + 3})^{2 x})

e^{8}

Decimal Notation

2980.95798 \dots

Solution steps

x \to \infty lim ((\frac{x + 7}{x + 3})^{2 x})

Apply exponent rules

= x \to \infty lim (e^{2 x l n (\frac{x + 7}{x + 3})})

Apply the Limit Chain Rule:

e^{8}

= e^{8}

x \to 0 lim (sin^{s i n (x)} (x))

x \to 0 + lim (\frac{1}{1 + 2 ^{\frac{1}{x}}})

x \to 5 lim (\frac{- 3}{x - 5})

x \to 2 - lim ((x - 2) \cdot ln (2 - x))

x \to 0 lim (\frac{x ^{3} - 3 x}{x})

What is the limit as x approaches infinity of ((x+7)/(x+3))^{2x} ?
The limit as x approaches infinity of ((x+7)/(x+3))^{2x} is e^8