Math  /  Calculus

QuestionFind the value of kk for the function f(x)={x+33x1x2x2kx=2f(x)=\left\{\begin{array}{ll}\frac{\sqrt{x+3}-\sqrt{3 x-1}}{x-2} & x \neq 2 \\ k & x=2\end{array}\right. to be continuous.

Studdy Solution
Evaluate the limit as xx approaches2.
k=122+332321=125325=225=15k = \frac{1}{2\sqrt{2+3}} - \frac{3}{2\sqrt{3*2-1}} = \frac{1}{2\sqrt{5}} - \frac{3}{2\sqrt{5}} = -\frac{2}{2\sqrt{5}} = -\frac{1}{\sqrt{5}}So, the value of kk that makes the function continuous at x=2x=2 is 15-\frac{1}{\sqrt{5}}.

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