Calculus Examples

$lim_{x \to 2} \frac{90 + 60 x}{x + 5}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2} 90 + 60 x}{lim_{x \to 2} x + 5}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2} 90 + lim_{x \to 2} 60 x}{lim_{x \to 2} x + 5}$

Step 3

Evaluate the limit of $90$ which is constant as $x$ approaches $2$ .

$\frac{90 + lim_{x \to 2} 60 x}{lim_{x \to 2} x + 5}$

Step 4

Move the term $60$ outside of the limit because it is constant with respect to $x$ .

$\frac{90 + 60 lim_{x \to 2} x}{lim_{x \to 2} x + 5}$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\frac{90 + 60 lim_{x \to 2} x}{lim_{x \to 2} x + lim_{x \to 2} 5}$

Step 6

Evaluate the limit of $5$ which is constant as $x$ approaches $2$ .

$\frac{90 + 60 lim_{x \to 2} x}{lim_{x \to 2} x + 5}$

Step 7

Evaluate the limits by plugging in $2$ for all occurrences of $x$ .

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Step 7.1

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\frac{90 + 60 \cdot 2}{lim_{x \to 2} x + 5}$

Step 7.2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\frac{90 + 60 \cdot 2}{2 + 5}$

Step 8

Simplify the answer.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Multiply $60$ by $2$ .

$\frac{90 + 120}{2 + 5}$

Step 8.1.2

Add $90$ and $120$ .

$\frac{210}{2 + 5}$

Step 8.2

Add $2$ and $5$ .

$\frac{210}{7}$

Step 8.3

Divide $210$ by $7$ .

$30$