Calculus Examples

$lim_{x \to 4^{+}} x^{3} - c x$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4^{+}} x^{3} - lim_{x \to 4^{+}} c x$

Step 2

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

${(lim_{x \to 4^{+}} x)}^{3} - lim_{x \to 4^{+}} c x$

Step 3

Move the term $c$ outside of the limit because it is constant with respect to $x$ .

${(lim_{x \to 4^{+}} x)}^{3} - c lim_{x \to 4^{+}} x$

Step 4

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4^{3} - c lim_{x \to 4^{+}} x$

Step 4.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4^{3} - c \cdot 4$

Step 5

Simplify each term.

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Step 5.1

Raise $4$ to the power of $3$ .

$64 - c \cdot 4$

Step 5.2

Multiply $4$ by $- 1$ .

$64 - 4 c$