Calculus Examples

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

Step 1

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

$lim_{x \to 49} x + 49 \cdot lim_{x \to 49} \sqrt{x} - 7$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Move the limit under the radical sign.

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

Step 6

Evaluate the limit of $7$ which is constant as $x$ approaches $49$ .

$(lim_{x \to 49} x + 49) \cdot (\sqrt{lim_{x \to 49} x} - 1 \cdot 7)$

Step 7

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

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Step 7.1

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

$(49 + 49) \cdot (\sqrt{lim_{x \to 49} x} - 1 \cdot 7)$

Step 7.2

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

$(49 + 49) \cdot (\sqrt{49} - 1 \cdot 7)$

Step 8

Simplify the answer.

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Step 8.1

Add $49$ and $49$ .

$98 \cdot (\sqrt{49} - 1 \cdot 7)$

Step 8.2

Simplify each term.

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Step 8.2.1

Rewrite $49$ as $7^{2}$ .

$98 \cdot (\sqrt{7^{2}} - 1 \cdot 7)$

Step 8.2.2

Pull terms out from under the radical, assuming positive real numbers.

$98 \cdot (7 - 1 \cdot 7)$

Step 8.2.3

Multiply $- 1$ by $7$ .

$98 \cdot (7 - 7)$

Step 8.3

Subtract $7$ from $7$ .

$98 \cdot 0$

Step 8.4

Multiply $98$ by $0$ .

$0$