What is the limit as x approaches 0+of (e+1/x)^x ?

The limit as x approaches 0+of (e+1/x)^x is 1

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limit as x approaches 0+of (e+1/x)^x

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

1

Solution steps

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

Apply exponent rules

= x \to 0 + lim (e^{x l n (e + \frac{1}{x})})

Apply the Limit Chain Rule:

1

= 1

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

x \to - π lim (cos (x))

x \to - 5 lim (cos (- 3 π x))

x \to π lim (ln (sin (\frac{x}{2})))

x \to \frac{π}{2} lim (1 + cos (x))

What is the limit as x approaches 0+of (e+1/x)^x ?
The limit as x approaches 0+of (e+1/x)^x is 1