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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If the function $f(x)=\left\{\begin{array}{cc}3 x-8, & \text { if } x \leq 5 \\ 2 k, & \text { if } x>5\end{array}\right.$ is continuous, then the value of $k$ is
  • A
    $2 / 7$
  • B
    $7 / 2$
  • C
    $3 / 7$
  • D
    $4 / 7$
✓

Answer

$\begin{array}{l}\text { : Since } f(x) \text { is continuous at } x=5 \text {, } \\ \Rightarrow \lim _{x \rightarrow 5} f(x)=\lim _{x \rightarrow 5^{+}} f(x)=f(5) \\ \Rightarrow \quad 3(5)-8=2 k \Rightarrow 7=2 k \Rightarrow k=\frac{7}{2}\end{array}$

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