Calculus Examples

$lim_{x \to 2} 2 x + 1$

Step 1

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

$lim_{x \to 2^{+}} 2 x + 1$

Step 2

Evaluate the limit.

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Step 2.1

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

$lim_{x \to 2^{+}} 2 x + lim_{x \to 2^{+}} 1$

Step 2.2

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to 2^{+}} x + lim_{x \to 2^{+}} 1$

Step 2.3

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$2 lim_{x \to 2^{+}} x + 1$

Step 3

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

$2 \cdot 2 + 1$

Step 4

Simplify the answer.

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Step 4.1

Multiply $2$ by $2$ .

$4 + 1$

Step 4.2

Add $4$ and $1$ .

$5$