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

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

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

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

\infty

Solution steps

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

Apply exponent rules

= x \to \infty lim (e^{(x + 2) l n (x + 1)})

Apply the Limit Chain Rule:

\infty

= \infty

\frac{d x}{d t} = \frac{4 x ^{2} + 7 t 4 t ^{2} + x ^{2}}{4 t x}

\frac{d}{d x} (- \frac{81}{( 1 + 9 x ) ^{2}})

y = 5 x^{2}, y = 30 x - 45, [0, 45]

y^{^{''}} + 25 y = cos (5 t)

Y = Y = ln (x - 3)

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