Calculus Examples

$lim_{x \to 200^{-}} {(3 - 0.015 x)}^{2}$

Step 1

Evaluate the limit.

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Step 1.1

Move the exponent $2$ from ${(3 - 0.015 x)}^{2}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 200^{-}} 3 - 0.015 x)}^{2}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $200$ .

${(lim_{x \to 200^{-}} 3 - lim_{x \to 200^{-}} 0.015 x)}^{2}$

Step 1.3

Evaluate the limit of $3$ which is constant as $x$ approaches $200$ .

${(3 - lim_{x \to 200^{-}} 0.015 x)}^{2}$

Step 1.4

Move the term $0.015$ outside of the limit because it is constant with respect to $x$ .

${(3 - 0.015 lim_{x \to 200^{-}} x)}^{2}$

Step 2

Evaluate the limit of $x$ by plugging in $200$ for $x$ .

${(3 - 0.015 \cdot 200)}^{2}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 0.015$ by $200$ .

${(3 - 3)}^{2}$

Step 3.2

Subtract $3$ from $3$ .

$0^{2}$

Step 3.3

Raising $0$ to any positive power yields $0$ .

$0$