Calculus Examples

$lim_{x \to 3} \frac{10}{x - 2}$

Step 1

Change the two-sided limit into a right sided limit.

$lim_{x \to 3^{+}} \frac{10}{x - 2}$

Step 2

Evaluate the limit.

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Step 2.1

Move the term $10$ outside of the limit because it is constant with respect to $x$ .

$10 lim_{x \to 3^{+}} \frac{1}{x - 2}$

Step 2.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $3$ .

$10 \frac{lim_{x \to 3^{+}} 1}{lim_{x \to 3^{+}} x - 2}$

Step 2.3

Evaluate the limit of $1$ which is constant as $x$ approaches $3$ .

$10 \frac{1}{lim_{x \to 3^{+}} x - 2}$

Step 2.4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3$ .

$10 \frac{1}{lim_{x \to 3^{+}} x - lim_{x \to 3^{+}} 2}$

Step 2.5

Evaluate the limit of $2$ which is constant as $x$ approaches $3$ .

$10 \frac{1}{lim_{x \to 3^{+}} x - 1 \cdot 2}$

Step 3

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$10 \frac{1}{3 - 1 \cdot 2}$

Step 4

Simplify the answer.

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Step 4.1

Simplify the denominator.

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Step 4.1.1

Multiply $- 1$ by $2$ .

$10 \frac{1}{3 - 2}$

Step 4.1.2

Subtract $2$ from $3$ .

$10 (\frac{1}{1})$

Step 4.2

Cancel the common factor of $1$ .

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Step 4.2.1

Cancel the common factor.

$10 (\frac{1}{1})$

Step 4.2.2

Rewrite the expression.

$10 \cdot 1$

Step 4.3

Multiply $10$ by $1$ .

$10$