Calculus Examples

lim_{x \to 1} {(\frac{x^{2} - 4 x^{2}}{x^{2} + x - 2})}^{3}

$lim_{x \to 1} {(\frac{x^{2} - 4 x^{2}}{x^{2} + x - 2})}^{3}$

Step 1

Subtract

4 x^{2}

$4 x^{2}$ from

x^{2}

$x^{2}$ .

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

$lim_{x \to 1} {(\frac{- 3 x^{2}}{x^{2} + x - 2})}^{3}$

Step 2

Consider the left sided limit.

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

$lim_{x \to 1^{-}} {(\frac{- 3 x^{2}}{x^{2} + x - 2})}^{3}$

Step 3

As the

x

$x$ values approach

1

$1$ from the left, the function values increase without bound.

\infty

$\infty$

Step 4

Consider the right sided limit.

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

$lim_{x \to 1^{+}} {(\frac{- 3 x^{2}}{x^{2} + x - 2})}^{3}$

Step 5

As the

x

$x$ values approach

1

$1$ from the right, the function values decrease without bound.

- \infty

$- \infty$

Step 6

Since the left sided and right sided limits are not equal, the limit does not exist.

Does not exist

$Does not exist$

lim_{x \to 1} ({(\frac{x^{2} - 4 x^{2}}{x^{2} + x - 2})}^{3})

$lim_{x \to 1} ({(\frac{x^{2} - 4 x^{2}}{x^{2} + x - 2})}^{3})$

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