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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY1 Mark
MCQ
The value of a for which the function $\text{f(x)}=\begin{cases}5\text{x}-4,&\text{if }0<\text{x}\leq1\\4\text{x}^2+3\text{ax},&\text{if }<\text{x}<2\end{cases}$ is continuous at every point of its domain, is:
  • A
    $\frac{13}{3}$
  • B
    1
  • C
    0
  • ✓
    -1
✓

Answer

Correct option: D.
-1
$\lim\limits_{\text{x}\rightarrow1^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow1^+}\text{f(x)}$

$\lim\limits_{\text{x}\rightarrow1}5\text{x}-4=\lim\limits_{\text{x}\rightarrow1}4\text{x}^2+3\text{ax}$

$1=4+3\text{a}$

$\text{a}=-1$

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