What is the limit as x approaches 1 of (x^{15}-1)/(x^5-1) ?

The limit as x approaches 1 of (x^{15}-1)/(x^5-1) is 3

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limit as x approaches 1 of (x^{15}-1)/(x^5-1)

x \to 1 lim (\frac{x ^{15} - 1}{x ^{5} - 1})

3

Solution steps

x \to 1 lim (\frac{x ^{15} - 1}{x ^{5} - 1})

Simplify

\frac{x ^{15} - 1}{x ^{5} - 1} : x^{10} + x^{5} + 1

= x \to 1 lim (x^{10} + x^{5} + 1)

Plug in the value

x = 1

= 1^{10} + 1^{5} + 1

Simplify

= 3

(\frac{1}{1 - cos ( x )})^{^{'}}

(\frac{1}{x ^{2} + 1})^{^{'}}

\frac{\partial}{\partial x} (sin (2 y x))

\frac{d y}{d x} = \frac{2 y}{5 y - 2 x}

What is the limit as x approaches 1 of (x^{15}-1)/(x^5-1) ?
The limit as x approaches 1 of (x^{15}-1)/(x^5-1) is 3