Calculus Examples

$\frac{lim_{y \to 2} y + 2}{y^{2} + 5 y + 6}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\frac{lim_{y \to 2} y + lim_{y \to 2} 2}{y^{2} + 5 y + 6}$

Step 1.2

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

$\frac{lim_{y \to 2} y + 2}{y^{2} + 5 y + 6}$

Step 2

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

$\frac{2 + 2}{y^{2} + 5 y + 6}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Add $2$ and $2$ .

$\frac{4}{y^{2} + 5 y + 6}$

Step 3.2

Factor $y^{2} + 5 y + 6$ using the AC method.

Tap for more steps...

Step 3.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $5$ .

$2, 3$

Step 3.2.2

Write the factored form using these integers.

$\frac{4}{(y + 2) (y + 3)}$