Calculus Examples

$lim_{x \to 3} \frac{3 - x}{x + 4}$

Step 1

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

$\frac{lim_{x \to 3} 3 - x}{lim_{x \to 3} x + 4}$

Step 2

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

$\frac{lim_{x \to 3} 3 - lim_{x \to 3} x}{lim_{x \to 3} x + 4}$

Step 3

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

$\frac{3 - lim_{x \to 3} x}{lim_{x \to 3} x + 4}$

Step 4

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

$\frac{3 - lim_{x \to 3} x}{lim_{x \to 3} x + lim_{x \to 3} 4}$

Step 5

Evaluate the limit of $4$ which is constant as $x$ approaches $3$ .

$\frac{3 - lim_{x \to 3} x}{lim_{x \to 3} x + 4}$

Step 6

Evaluate the limits by plugging in $3$ for all occurrences of $x$ .

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Step 6.1

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

$\frac{3 - 3}{lim_{x \to 3} x + 4}$

Step 6.2

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

$\frac{3 - 3}{3 + 4}$

Step 7

Simplify the answer.

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Step 7.1

Subtract $3$ from $3$ .

$\frac{0}{3 + 4}$

Step 7.2

Add $3$ and $4$ .

$\frac{0}{7}$

Step 7.3

Divide $0$ by $7$ .

$0$