For , determine the value of that satisfies…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For k>0k>0, determine the value of kk that satisfies lim⁡x→1kx+1−k+1x−1=13\displaystyle \lim_{x \to 1} \frac{\sqrt{kx+1}-\sqrt{k+1}}{x-1}=\dfrac{1}{3}. (a) 2(1+13)9\dfrac{2\bigl(1+\sqrt{13}\bigr)}{9} (b) 2(1+10)9\dfrac{2\bigl(1+\sqrt{10}\bigr)}{9} (c) 1+109\dfrac{1+\sqrt{10}}{9} (d) 54\dfrac{5}{4}

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