Calculus Examples

$lim_{x \to 1} 2 - \frac{5}{{(x - 1)}^{2}}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} 2 - lim_{x \to 1} \frac{5}{{(x - 1)}^{2}}$

Step 1.2

Evaluate the limit of $2$ which is constant as $x$ approaches $1$ .

$2 - lim_{x \to 1} \frac{5}{{(x - 1)}^{2}}$

Step 2

Since the numerator is positive and the denominator ${(x - 1)}^{2}$ approaches zero and is greater than zero for $x$ near $1$ on both sides, the function increases without bound.

$2 - \infty$

Step 3

Simplify the answer.

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Step 3.1

A non-zero constant times infinity is infinity.

$2 + - \infty$

Step 3.2

Infinity plus or minus a number is infinity.

$- \infty$