Evaluate the limit: _x 4 sqrt(x) - 2sqrt(x) - 4

May 14, 2026Mathematics

ScanSolve AI Answer

May 14, 2026

Answer

Step 1: Substitute $x=4$ into the expression to check for an indeterminate form. Substitute $x=4$ into the numerator: $\sqrt{4} - 2 = 2 - 2 = 0$ Substitute $x=4$ into the denominator: $\sqrt{4} - 4 = 2 - 4 = -2$

Step 2: Evaluate the limit. Since the denominator is not zero when $x=4$ , we can directly substitute the value of $x$ into the expression to find the limit. $\lim_{x \to 4} \frac{\sqrt{x} - 2}{\sqrt{x} - 4} = \frac{0}{-2}$ $= 0$

The final answer is $\boxed{0}$ .

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Quick Answer

Substitute x=4 into the numerator: sqrt(4) - 2 = 2 - 2 = 0 Substitute x=4 into the denominator: sqrt(4) - 4 = 2 - 4 = -2 Step 2: Evaluate the limit.
Since the denominator is not zero when x=4, we can directly substitute the value of x into the expression to find the limit.
_x 4 sqrt(x) - 2sqrt(x) - 4 = (0)/(-2) = 0 The final answer is 0.
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Asked on May 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 14, 2026

Step 1: Substitute x=4 into the expression to check for an indeterminate form. Substitute x=4 into the numerator: sqrt(4) - 2 = 2 - 2 = 0 Substitute x=4 into the denominator: sqrt(4) - 4 = 2 - 4 = -2 Step 2: Evaluate the limit. Since the denominator is not zero when x=4, we can directly substitute the value of x into the expression to find the limit. _x 4 sqrt(x) - 2sqrt(x) - 4 = (0)/(-2) = 0 The final answer is 0. 3 done, 2 left today. You're making progress.