Calculus Examples

$f (x) = e^{x}$ , $a = 0$

Step 1

Consider the function used to find the linearization at $a$ .

$L (x) = f (a) + f' (a) (x - a)$

Step 2

Substitute the value of $a = 0$ into the linearization function.

$L (x) = f (0) + f' (0) (x - 0)$

Step 3

Evaluate $f (0)$ .

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Step 3.1

Replace the variable $x$ with $0$ in the expression.

$f (0) = e^{0}$

Step 3.2

Simplify $e^{0}$ .

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Step 3.2.1

Remove parentheses.

$e^{0}$

Step 3.2.2

Anything raised to $0$ is $1$ .

$1$

Step 4

Substitute the components into the linearization function in order to find the linearization at $a$ .

$L (x) = 1 + 1 (x - 0)$

Step 5

Simplify each term.

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Step 5.1

Multiply $x - 0$ by $1$ .

$L (x) = 1 + x - 0$

Step 5.2

Subtract $0$ from $x$ .

$L (x) = 1 + x$

Step 6