Calculus Examples

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

Step 1

Subtract $4 x^{2}$ from $x^{2}$ .

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

Step 2

Consider the left sided limit.

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

Step 3

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

$\infty$

Step 4

Consider the right sided limit.

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

Step 5

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

$- \infty$

Step 6

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

$Does not exist$