If f(x)= l 2x+b(x< ) +d( x ) . is such that _ x a f(x=L),then L. - Vidyadip

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

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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Limits and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

The value of $\frac{\cos3\text{x}}{2\cos2\text{x}-1}$ is equal to:

In polar representation of a complex number $\Big(\text{r},\frac{\pi}{2}\Big)$lies on ____________?

If $f(x)=\frac{2 x+c}{x-1}$ and $f^{\prime}(0)=0$, then value of $c$ is equal to :

$\sum\limits^{16}_{\text{r}+2}{^{16}}\text{C}_\text{r}=$

If $\text{f(x)}=\frac{\sin^{4}\text{x}+\cos^2\text{x}}{\sin^2\text{x}+\cos^4\text{x}}$ for $\text{x}\in\text{R},$ then f(2002) =

1
2
3
4

Choose the correct answer.
If – 3x + 17 < – 13, then:

If 2x + 1 > 5 then which is true?

The parametric equations of a parabola are x = t² + 1, y = 2t + 1. The cartesian equation of its directrix is

x = 0
x + 1 = 0
y = 0
None of these

If $\frac{1-\text{ix}}{1+\text{ix}}=\text{a}+\text{ib},$ then $\text{a}^2+\text{b}^2=$

If a + 2b + 3c = 12 , (a, b, c ∈ R+), then ab²c³ is: