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/Evaluate lim₍ₓ→0₎ ( √(1 + 2x) − √(1 &minu...

Question

Evaluate lim₍ₓ→0₎ ( √(1 + 2x) − √(1 − 3x) ) / x

A 5/2 Correct Incorrect

B 2/3 Correct Incorrect

C 1/3 Correct Incorrect

D 1/4 Correct Incorrect

Detailed Solution

Multiply by conjugate: = [(√(1 + 2x) − √(1 − 3x)) × (√(1 + 2x) + √(1 − 3x))] / [x(√(1 + 2x) + √(1 − 3x))] = [(1 + 2x) − (1 − 3x)] / [x(√(1 + 2x) + √(1 − 3x))] = [5x] / [x(√(1 + 2x) + √(1 − 3x))] = 5 / [√(1 + 2x) + √(1 − 3x)] Now put x = 0 → denominator = 1 + 1 = 2 Answer: 5 / 2

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