Consider the following expression. \(\displaystyle…
2021
Consider the following expression.
\(\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}\)
he value of the above expression (rounded to 2 decimal places) is ___________.
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Correct answer: 0.25
Evaluate the limit: Limit as x → -3 of (sqrt(2x + 22) - 4) / (x + 3).
Multiply numerator and denominator by the conjugate of the numerator: (sqrt(2x + 22) + 4) / (sqrt(2x + 22) + 4).
The numerator becomes (2x + 22) - 16 = 2x + 6 = 2(x + 3). The denominator becomes (x + 3)(sqrt(2x + 22) + 4).
Cancel the common factor (x + 3) for x ≠ -3 to get the simplified expression 2 / (sqrt(2x + 22) + 4).
Now substitute x = -3: sqrt(2(−3) + 22) = sqrt(16) = 4, so the value is 2 / (4 + 4) = 2/8 = 1/4 = 0.25.
Final answer (rounded to 2 decimal places): 0.25