Download App

STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 1} \frac{{1 + \log x - x}}{{1 - 2x + {x^2}}} = $
  • A
    $1$
  • B
    $-1$
  • C
    $0$
  • ✓
    $ - \frac{1}{2}$
✓

Answer

Correct option: D.
$ - \frac{1}{2}$
d
(d) Applying $ L- $Hospital’s rule,

$\mathop {{\rm{lim}}}\limits_{x \to 1} \,\,\frac{{1 + \log x - x}}{{1 - 2x + {x^2}}} = \mathop {{\rm{lim}}}\limits_{x \to 1} \,\,\frac{{\frac{1}{x} - 1}}{{ - 2 + 2x}} = \mathop {{\rm{lim}}}\limits_{x \to 1} \,\,\frac{{1 - x}}{{2x(x - 1)}}$

Again applying $ L-$ Hospital’s rule,

$\mathop {{\rm{lim}}}\limits_{x \to 1} \frac{{ - 1}}{{4x - 2}} = - \frac{1}{2}$.

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 STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The equation of the circle passing through $(1,0)$ and $(0,1)$ and having smallest possible radius is :-
→
The equation of circle whose centre lies on $3x - y - 4 = 0$ and$x + 3y + 2 = 0$ and has an area $154$ square units is
→
The coefficient of $x^{4}$ in the expansion of $\left(1+x+x^{2}+x^{3}\right)^{6}$ in powers of $x,$ is
→
The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$, is :
→
$\mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos mx}}{{1 - \cos nx}} = $
→
If $\alpha $ is an imaginary cube root of unity, then for $n \in N$, the value of ${\alpha ^{3n + 1}} + {\alpha ^{3n + 3}} + {\alpha ^{3n + 5}}$ is
→
$\sin^2\frac{\pi}{18}+\sin^2\frac{\pi}{9}+\sin^2\frac{7\pi}{18}+\sin^2\frac{4\pi}{9}=$
→
If $ \text{z}=\Big(\frac{\sqrt{3}}{2}+\frac{\text{i}}{2}\Big)5+\Big(\frac{\sqrt{3}}{2}-\frac{\text{i}}{2}\Big)5,$ then:
→
If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be
→
$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0,$ then $\theta = $
→