Calculus Examples

$lim_{h \to a} (1 - 2 (a + h)) - (1 - 2 a)$

Step 1

Evaluate the limit of $(1 - 2 (a + h)) - (1 - 2 a)$ by plugging in $a$ for $h$ .

$1 - 2 (a + a) - (1 - 2 a)$

Step 2

Simplify each term.

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Step 2.1

Add $a$ and $a$ .

$1 - 2 (2 a) - (1 - 2 a)$

Step 2.2

Multiply $2$ by $- 2$ .

$1 - 4 a - (1 - 2 a)$

Step 2.3

Apply the distributive property.

$1 - 4 a - 1 \cdot 1 - (- 2 a)$

Step 2.4

Multiply $- 1$ by $1$ .

$1 - 4 a - 1 - (- 2 a)$

Step 2.5

Multiply $- 2$ by $- 1$ .

$1 - 4 a - 1 + 2 a$

Step 3

Combine the opposite terms in $1 - 4 a - 1 + 2 a$ .

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Step 3.1

Subtract $1$ from $1$ .

$- 4 a + 0 + 2 a$

Step 3.2

Add $- 4 a$ and $0$ .

$- 4 a + 2 a$

Step 4

Add $- 4 a$ and $2 a$ .

$- 2 a$