Which of the following limits

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Which of the following limits, if it exists, equals the slope of the line tangent to the graph of y=xy=\sqrt{x} at x=4x=4? (a) lim⁡x→4x−4x+4\displaystyle \lim_{x\to 4}\frac{\sqrt{x}-\sqrt{4}}{x+4} (b) lim⁡h→04+h−4h\displaystyle \lim_{h\to 0}\frac{\sqrt{4+h}-\sqrt{4}}{h} (c) lim⁡h→04+h−44+h\displaystyle \lim_{h\to 0}\frac{\sqrt{4+h}-\sqrt{4}}{4+h} (d) lim⁡x→4x−4(x−4)2\displaystyle \lim_{x\to 4}\frac{\sqrt{x}-\sqrt{4}}{(x-4)^{2}}

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