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

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

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limit as x approaches 1 of (x^2-sqrt(x))/(1-x)

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

- \frac{3}{2}

Decimal Notation

- 1.5

Solution steps

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

Multiply by the conjugate of

x^{2} - x : \frac{x ^{4} - x}{x ^{2} + x}

= x \to 1 lim \frac{\frac{x ^{4} - x}{x ^{2} + x}}{1 - x}

Simplify

\frac{\frac{x ^{4} - x}{x ^{2} + x}}{1 - x} : - \frac{x ( x ^{2} + x + 1 )}{x ^{2} + x}

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

Plug in the value

x = 1

= - \frac{1 \cdot ( 1 ^{2} + 1 + 1 )}{1 ^{2} + 1}

Simplify

- \frac{1 \cdot ( 1 ^{2} + 1 + 1 )}{1 ^{2} + 1} : - \frac{3}{2}

= - \frac{3}{2}

\int \frac{3 ^{2 x}}{1 + 3 ^{2 x}} d x

x \to \infty lim (tan (\frac{7}{x}))

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

\int (e^{x} x) d x

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