What is the limit as x approaches 0 of (e^x+x)^{1/2} ?

The limit as x approaches 0 of (e^x+x)^{1/2} is 1

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limit as x approaches 0 of (e^x+x)^{1/2}

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

1

Solution steps

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

Plug in the value

x = 0

= (e^{0} + 0)^{\frac{1}{2}}

Simplify

= 1

x \to \infty lim (4 x^{2} + 2 x + 2 x)

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

x \to \infty lim (0 xx)

x \to 0 lim (x^{2} cot (4 x^{2}))

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

What is the limit as x approaches 0 of (e^x+x)^{1/2} ?
The limit as x approaches 0 of (e^x+x)^{1/2} is 1