Exercise 1.4.21

Question

If $f(x)=5^{x}$, show that
  $$\frac{f(x+h)-f(x)}{h}=5^{x}\left(\frac{5^{h}-1}{h}\right).$$

Khagan Gulusoy · Accepted Answer

$$\frac{f(x+h)-f(x)}{h}=\frac{5^{x+h}-5^{x}}{h}=\frac{5^{x} \cdot 5^{h}-5^{x}}{h}=\frac{5^{x}\left(5^{h}-1\right)}{h}=5^{x} \cdot\left(\frac{5^{h}-1}{h}\right).\ \square$$

Exercise 1.4.21

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Exercise 1.4.21

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