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

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

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limit as x approaches 1 of ((x^5-1))/(x^3-1)

x \to 1 lim (\frac{( x ^{5} - 1 )}{x ^{3} - 1})

\frac{5}{3}

Decimal Notation

1.66666 \dots

Solution steps

x \to 1 lim (\frac{x ^{5} - 1}{x ^{3} - 1})

Simplify

\frac{x ^{5} - 1}{x ^{3} - 1} : \frac{x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{2} + x + 1}

= x \to 1 lim (\frac{x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{2} + x + 1})

Plug in the value

x = 1

= \frac{1 ^{4} + 1 ^{3} + 1 ^{2} + 1 + 1}{1 ^{2} + 1 + 1}

Simplify

= \frac{5}{3}

- 0.025 x^{2} + 4 x

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

\int (5^{3 x} + cosh (x)) d x

x \to 3 lim (2^{x})

\int tan^{5} (x) sec^{9} (x) d x

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