Calculus Examples

$\frac{lim_{x \to 49} (f (x)) (49 - x)}{7 - \sqrt{x}}$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $49$ .

$\frac{lim_{x \to 49} f (x) \cdot lim_{x \to 49} 49 - x}{7 - \sqrt{x}}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $49$ .

$\frac{lim_{x \to 49} f (x) \cdot (lim_{x \to 49} 49 - lim_{x \to 49} x)}{7 - \sqrt{x}}$

Step 3

Evaluate the limit of $49$ which is constant as $x$ approaches $49$ .

$\frac{lim_{x \to 49} f (x) \cdot (49 - lim_{x \to 49} x)}{7 - \sqrt{x}}$

Step 4

Evaluate the limits by plugging in $49$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $f (x)$ by plugging in $49$ for $x$ .

$\frac{f (49) \cdot (49 - lim_{x \to 49} x)}{7 - \sqrt{x}}$

Step 4.2

Evaluate the limit of $x$ by plugging in $49$ for $x$ .

$\frac{f (49) \cdot (49 - 49)}{7 - \sqrt{x}}$

Step 5

Simplify the answer.

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Step 5.1

Subtract $49$ from $49$ .

$\frac{f (49) \cdot 0}{7 - \sqrt{x}}$

Step 5.2

Multiply $f (49)$ by $0$ .

$\frac{0}{7 - \sqrt{x}}$

Step 5.3

Divide $0$ by $7 - \sqrt{x}$ .

$0$