Calculus Examples

$lim_{x \to 1} x - \frac{1}{| x - 1 |}$

Step 1

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

$lim_{x \to 1} x - lim_{x \to 1} \frac{1}{| x - 1 |}$

Step 2

Since the numerator is positive and the denominator $| x - 1 |$ approaches zero and is greater than zero for $x$ near $1$ on both sides, the function increases without bound.

$lim_{x \to 1} x - \infty$

Step 3

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$1 - \infty$

Step 4

Simplify the answer.

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Step 4.1

A non-zero constant times infinity is infinity.

$1 + - \infty$

Step 4.2

Infinity plus or minus a number is infinity.

$- \infty$