Calculus Examples

$lim_{x \to 1} f (x) x^{3} - 5$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} f (x) x^{3} - lim_{x \to 1} 5$

Step 2

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} f (x) \cdot lim_{x \to 1} x^{3} - lim_{x \to 1} 5$

Step 3

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

$lim_{x \to 1} f (x) \cdot {(lim_{x \to 1} x)}^{3} - lim_{x \to 1} 5$

Step 4

Evaluate the limit of $5$ which is constant as $x$ approaches $1$ .

$lim_{x \to 1} f (x) \cdot {(lim_{x \to 1} x)}^{3} - 1 \cdot 5$

Step 5

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $f (x)$ by plugging in $1$ for $x$ .

$f (1) \cdot {(lim_{x \to 1} x)}^{3} - 1 \cdot 5$

Step 5.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$f (1) \cdot 1^{3} - 1 \cdot 5$

Step 6

Simplify each term.

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Step 6.1

One to any power is one.

$f (1) \cdot 1 - 1 \cdot 5$

Step 6.2

Multiply $f (1)$ by $1$ .

$f (1) - 1 \cdot 5$

Step 6.3

Multiply $- 1$ by $5$ .

$f (1) - 5$