Calculus Examples

$f (x) = {\begin{cases} 8 & x < - 4 \\ - 10 + x^{2} & - 4 \leq x < 4 \\ 2 x - 2 & x \geq 4 \end{cases}$

Step 1

Find the limit of $8$ as $x$ approaches $- 4$ from the left.

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Step 1.1

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

$lim_{x \to {(- 4)}^{-}} 8$

Step 1.2

Evaluate the limit of $8$ which is constant as $x$ approaches $- 4$ .

$8$

Step 2

Evaluate $- 10 + x^{2}$ at $- 4$ .

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Step 2.1

Replace the variable $x$ with $- 4$ in the expression.

$- 10 + {(- 4)}^{2}$

Step 2.2

Evaluate.

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Step 2.2.1

Raise $- 4$ to the power of $2$ .

$- 10 + 16$

Step 2.2.2

Add $- 10$ and $16$ .

$6$

Step 3

Since the limit of $8$ as $x$ approaches $- 4$ from the left is not equal to the function value at $x = - 4$ , the function is not continuous at $x = - 4$ .

Not continuous

Step 4