Find the values of k so that the function f i | vedclass

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(A) For the function $f(x)$ to be continuous at $x=2$,the left-hand limit,right-hand limit,and the value of the function at $x=2$ must be equal.$1$. T

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$3/4$

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(A) For the function $f(x)$ to be continuous at $x=2$,the left-hand limit,right-hand limit,and the value of the function at $x=2$ must be equal.$1$. The value of the function at $x=2$ is $f(2) = k(2)^2 = 4k$.$2$. The left-hand limit at $x=2$ is $\lim_{x 	o 2^-} f(x) = \lim_{x 	o 2^-} (kx^2) = k(2)^2 = 4k$.$3$. The right-hand limit at $x=2$ is $\lim_{x 	o 2^+} f(x) = \lim_{x 	o 2^+} (3) = 3$.For continuity,$\lim_{x 	o 2^-} f(x) = \lim_{x 	o 2^+} f(x) = f(2)$.Therefore,$4k = 3$.Solving for $k$,we get $k = 3/4$.

Find the values of $k$ so that the function $f$ is continuous at the indicated point. $f(x) = \begin{cases} kx^2, & \text{if } x \le 2 \\ 3, & \text{if } x > 2 \end{cases}$ at $x=2$.

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