What is the limit as x approaches 2 of (x+1)^{x+3} ?

The limit as x approaches 2 of (x+1)^{x+3} is 243

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limit as x approaches 2 of (x+1)^{x+3}

x \to 2 lim ((x + 1)^{x + 3})

243

Solution steps

x \to 2 lim ((x + 1)^{x + 3})

Plug in the value

x = 2

= (2 + 1)^{2 + 3}

Simplify

= 243

x \to 0 + lim ((1 + \frac{6}{x})^{2 x})

x \to 8 lim (\frac{2}{x - 8})

x \to 0 + lim ((5 x)^{6 x})

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

x \to 0 + lim (x^{12 x})

What is the limit as x approaches 2 of (x+1)^{x+3} ?
The limit as x approaches 2 of (x+1)^{x+3} is 243