Calculus Examples

$lim_{h \to 0} (7 f (x + h)) - 7 f (x - h)$

Step 1

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

$lim_{h \to 0} 7 f (x + h) - lim_{h \to 0} 7 f (x - h)$

Step 2

Move the term $7$ outside of the limit because it is constant with respect to $h$ .

$7 lim_{h \to 0} f (x + h) - lim_{h \to 0} 7 f (x - h)$

Step 3

Move the term $7$ outside of the limit because it is constant with respect to $h$ .

$7 lim_{h \to 0} f (x + h) - 7 lim_{h \to 0} f (x - h)$

Step 4

Evaluate the limits by plugging in $0$ for all occurrences of $h$ .

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Step 4.1

Evaluate the limit of $f (x + h)$ by plugging in $0$ for $h$ .

$7 f (x + 0) - 7 lim_{h \to 0} f (x - h)$

Step 4.2

Add $x$ and $0$ .

$7 f (x) - 7 lim_{h \to 0} f (x - h)$

Step 4.3

Evaluate the limit of $f (x - h)$ by plugging in $0$ for $h$ .

$7 f (x) - 7 f (x + 0)$

Step 4.4

Add $x$ and $0$ .

$7 f (x) - 7 f (x)$

Step 5

Subtract $7 f (x)$ from $7 f (x)$ .

$0$