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Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives1 Mark
MCQ
If $ \mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2\mathrm{x}+\mathrm{b}(\mathrm{x}<\alpha)\\\mathrm{x}+\mathrm{d}(\mathrm{\text{x}}\geq\alpha)\end{array}\right.$ is such that $ \lim_\limits{\text{x} \rightarrow \text{a}}\text{f}(\text{x}=\text{L})$,then L.
  • A
    2d - b
  • B
    b - db
  • C
    d + bd
  • D
    b-  2d
✓

Answer

  1. 2d - b

Solution:

$ \begin{matrix}\lim\\\text{h}\rightarrow 0^{-} \end{matrix}\ \text{f(x)}=2(\alpha -\text{h})+\text{b}=2\alpha +\text{b}=\text{L} ............(1)$

$ \begin{matrix}\lim\\\text{h}\rightarrow 0 ^{+} \end{matrix}\text{ f(x)}=(\alpha +\text{h})+\text{d = L}\quad \quad \ \alpha =\text{L - d}\ ................(2)$
 

Substituting value of euation (2)in (1), we get

$ 2\left (\text{L}-\text{d} \right )+\text{b}=\text{L}$

L = 2d - b

Hence, option A is correct.

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