Calculus Examples

$lim_{h \to 0} 3 h + 6 x + 4$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $h$ approaches $0$ .

$lim_{h \to 0} 3 h + lim_{h \to 0} 6 x + lim_{h \to 0} 4$

Step 1.2

Move the term $3$ outside of the limit because it is constant with respect to $h$ .

$3 lim_{h \to 0} h + lim_{h \to 0} 6 x + lim_{h \to 0} 4$

Step 1.3

Evaluate the limit of $6 x$ which is constant as $h$ approaches $0$ .

$3 lim_{h \to 0} h + 6 x + lim_{h \to 0} 4$

Step 1.4

Evaluate the limit of $4$ which is constant as $h$ approaches $0$ .

$3 lim_{h \to 0} h + 6 x + 4$

Step 2

Evaluate the limit of $h$ by plugging in $0$ for $h$ .

$3 \cdot 0 + 6 x + 4$

Step 3

Simplify the answer.

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Step 3.1

Multiply $3$ by $0$ .

$0 + 6 x + 4$

Step 3.2

Add $0$ and $6 x$ .

$6 x + 4$