What is the limit as x approaches 0 of 5^x+x^5 ?

The limit as x approaches 0 of 5^x+x^5 is 1

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limit as x approaches 0 of 5^x+x^5

x \to 0 lim (5^{x} + x^{5})

1

Solution steps

x \to 0 lim (5^{x} + x^{5})

Plug in the value

x = 0

= 5^{0} + 0^{5}

Simplify

= 1

x \to 0 - lim (x^{2} - \frac{6}{x})

x \to 0 lim (cot (11 x))

x \to 0 + lim (3 (\frac{1}{x} - cot (x)))

x \to 1 lim (3 x - 5)

x \to 2 lim (\frac{5 x - 2}{x - 2})

What is the limit as x approaches 0 of 5^x+x^5 ?
The limit as x approaches 0 of 5^x+x^5 is 1