What is the limit as x approaches 0 of 5^{x+h}-5^x ?

The limit as x approaches 0 of 5^{x+h}-5^x is 5^h-1

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limit as x approaches 0 of 5^{x+h}-5^x

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

5^{h} - 1

Solution steps

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

Plug in the value

x = 0

= 5^{0 + h} - 5^{0}

Simplify

= 5^{h} - 1

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\int_{0}^{4} \frac{1}{x ^{2} + 9} d x

What is the limit as x approaches 0 of 5^{x+h}-5^x ?
The limit as x approaches 0 of 5^{x+h}-5^x is 5^h-1