What is the limit as x approaches 1 of (x^{3/2}-1)/(1-x) ?

The limit as x approaches 1 of (x^{3/2}-1)/(1-x) is -3/2

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limit as x approaches 1 of (x^{3/2}-1)/(1-x)

x \to 1 lim (\frac{x ^{\frac{3}{2}} - 1}{1 - x})

- \frac{3}{2}

Decimal Notation

- 1.5

Solution steps

x \to 1 lim (\frac{x ^{\frac{3}{2}} - 1}{1 - x})

Multiply by the conjugate of

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

= x \to 1 lim \frac{\frac{x ^{3} - 1}{x ^{\frac{3}{2}} + 1}}{1 - x}

Simplify

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

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

Plug in the value

x = 1

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

Simplify

= - \frac{3}{2}

\frac{d}{d x} ((sec (x))^{3})

3 \frac{d x}{d t} + x = 0.5

x^{\frac{99}{100}}

\frac{d}{d x} (d cos (t) + t^{2} sin (t))

f (x) = ln (x), at x = - \frac{1}{2}

What is the limit as x approaches 1 of (x^{3/2}-1)/(1-x) ?
The limit as x approaches 1 of (x^{3/2}-1)/(1-x) is -3/2