f(x)= cc 3 x-8, & if x 5 2 k, & if x>5 . is continuous at x=5, fi… - Vidyadip

MCQ

$f(x)=\left\{\begin{array}{cc}3 x-8, & \text { if } x \leq 5 \\ 2 k, & \text { if } x>5\end{array}\right.$ is continuous at $x=5$, find k .

A
$\frac{4}{7}$
B
$\frac{2}{7}$
✓
$\frac{7}{2}$
D
$\frac{3}{7}$

✓

Answer

Correct option: C.

$\frac{7}{2}$

(C)
$\lim _{x \rightarrow 5^{-}} f (x)=\lim _{x \rightarrow 5}(3 x-8)=7$
$\lim _{x \rightarrow 5^{+}} f (x)=\lim _{x \rightarrow 5} 2 k =2 k$
Since $f (x)$ is continuous at $x=5$.
$\therefore \quad \lim _{x \rightarrow 5^{-}} f (x)=\lim _{x \rightarrow 5^{+}} f (x)$
$\Rightarrow 7=2 k \Rightarrow k =\frac{7}{2}$

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