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

The limit as x approaches infinity of e^{xln(1+3/(2x))} is e^{3/2}

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limit as x approaches infinity of e^{xln(1+3/(2x))}

x \to \infty lim (e^{x l n (1 + \frac{3}{2 x})})

e^{\frac{3}{2}}

Decimal Notation

4.48168 \dots

Solution steps

x \to \infty lim (e^{x l n (1 + \frac{3}{2 x})})

Simplify

e^{x l n (1 + \frac{3}{2 x})} : (1 + \frac{3}{2 x})^{x}

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

Apply exponent rules

= x \to \infty lim (e^{x l n (1 + \frac{3}{2 x})})

Apply the Limit Chain Rule:

e^{\frac{3}{2}}

= e^{\frac{3}{2}}

x \to 0 + lim (\frac{ln ( 1 + 10 x )}{x})

x \to \infty lim (\frac{x}{s})

n \to 0 lim ((- \frac{3}{5})^{n})

h \to 0 lim (\frac{sin ( 2 x + h ) - sin ( 2 x )}{h})

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

What is the limit as x approaches infinity of e^{xln(1+3/(2x))} ?
The limit as x approaches infinity of e^{xln(1+3/(2x))} is e^{3/2}