Calculus Examples

$lim_{x \to 5} 0.75 x - 14.15 \sqrt{x} + 55.3$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$lim_{x \to 5} 0.75 x - lim_{x \to 5} 14.15 \sqrt{x} + lim_{x \to 5} 55.3$

Step 2

Move the term $0.75$ outside of the limit because it is constant with respect to $x$ .

$0.75 lim_{x \to 5} x - lim_{x \to 5} 14.15 \sqrt{x} + lim_{x \to 5} 55.3$

Step 3

Move the term $14.15$ outside of the limit because it is constant with respect to $x$ .

$0.75 lim_{x \to 5} x - 14.15 lim_{x \to 5} \sqrt{x} + lim_{x \to 5} 55.3$

Step 4

Move the limit under the radical sign.

$0.75 lim_{x \to 5} x - 14.15 \sqrt{lim_{x \to 5} x} + lim_{x \to 5} 55.3$

Step 5

Evaluate the limit of $55.3$ which is constant as $x$ approaches $5$ .

$0.75 lim_{x \to 5} x - 14.15 \sqrt{lim_{x \to 5} x} + 55.3$

Step 6

Evaluate the limits by plugging in $5$ for all occurrences of $x$ .

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Step 6.1

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$0.75 \cdot 5 - 14.15 \sqrt{lim_{x \to 5} x} + 55.3$

Step 6.2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$0.75 \cdot 5 - 14.15 \sqrt{5} + 55.3$

Step 7

Simplify the answer.

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Step 7.1

Simplify each term.

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Step 7.1.1

Multiply $0.75$ by $5$ .

$3.75 - 14.15 \sqrt{5} + 55.3$

Step 7.1.2

Multiply $- 14.15$ by $\sqrt{5}$ .

$3.75 - 31.64036188 + 55.3$

Step 7.2

Subtract $31.64036188$ from $3.75$ .

$- 27.89036188 + 55.3$

Step 7.3

Add $- 27.89036188$ and $55.3$ .

$27.40963811$