What is the limit as x approaches infinity of (1+3/x)^{x/4} ?

The limit as x approaches infinity of (1+3/x)^{x/4} is e^{3/4}

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limit as x approaches infinity of (1+3/x)^{x/4}

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

e^{\frac{3}{4}}

Decimal Notation

2.11700 \dots

Solution steps

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{4} l n (1 + \frac{3}{x})})

Apply the Limit Chain Rule:

e^{\frac{3}{4}}

= e^{\frac{3}{4}}

h (x) = ln (x + x^{2} - 7)

\frac{- 2 s + 1}{s ^{2} + 2 s - 8}

x \to 0 lim (\frac{x + 4}{x})

\int \frac{3}{( x + 5 ) ^{2} + 4} d x

\frac{d}{d x} (e sin (x))

What is the limit as x approaches infinity of (1+3/x)^{x/4} ?
The limit as x approaches infinity of (1+3/x)^{x/4} is e^{3/4}