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Evaluate the limit: lim (2x - 1) * sqrt(x+4) as x approaches 0.

Mathematics

ScanSolve AI Answer

Answer

-2

Step-by-step solution

2 steps
  1. Substitute x=0x=0 into the expression.

    Since the function (2x−1)x+4(2x - 1)\sqrt{x+4} is continuous at x=0x=0, we can evaluate the limit by direct substitution.

    lim⁡x→0(2x−1)x+4=(2(0)−1)0+4\lim_{x \to 0} (2x - 1)\sqrt{x+4} = (2(0) - 1)\sqrt{0+4}
  2. Simplify the expression.

    (0−1)4(0 - 1)\sqrt{4} (−1)(2)(-1)(2) −2-2
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