If the function f(x)= c _ e (1-x+x^ 2 )+ _ e (1+x+x^ 2 ) x- x , x… - Vidyadip

MCQ

If the function $f(x)=\left\{\begin{array}{c}\frac{\log _{e}\left(1-x+x^{2}\right)+\log _{e}\left(1+x+x^{2}\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\ k \end{array}\right.$ is continuous at $x =0$, then $k$ is equal to.

✓
$1$
B
$-1$
C
$e$
D
$0$

✓

Answer

Correct option: A.

$1$

a
$\lim _{x \rightarrow 0} \frac{\left(\ln \left(1+x^{2}+x^{4}\right)\right) \cos x}{1-\cos ^{2} x}$

$\lim _{x \rightarrow 0} \frac{\left(\frac{\ln \left(1+x^{2}+x^{4}\right)}{x^{2}+x^{4}}\right) x^{2}\left(1+x^{2}\right) \cos x}{\left(\frac{\sin ^{2} x}{x^{2}}\right) x^{2}}=1$

$\therefore k =1$

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

Suppose that $A, B, C$ are events such that $P\,(A) = P\,(B) = P\,(C) = \frac{1}{4},\,P\,(AB) = P\,(CB) = 0,\,P\,(AC) = \frac{1}{8},$ then $P\,(A + B) = $

The sum of $\left(1^2-1+1\right)(1 !)+\left(2^2-2+1\right)(2 !)$ $+\ldots+\left(n^2-n+1\right)(n !)$ is

The sum of three consecutive terms in a geometric progression is $14$. If $1$ is added to the first and the second terms and $1$ is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is

If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is

A circle touches the axes at the points $(3, 0)$ and $(0, -3)$. The centre of the circle is

The value of $\mathop {\lim }\limits_{x \to a} \frac{{\log (x - a)}}{{\log ({e^x} - {e^a})}}$ is

In a triangle $P Q R, P$ is the largest angle and $\cos P=\frac{1}{3}$. Further the incircle of the triangle touches the sides $P Q, Q R$ and $R P$ at $N, L$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive even integers. Then possible length$(s)$ of the side$(s)$ of the triangle is (are)

$(A)$ $16$ $(B)$ $18$ $(C)$ $24$ $(D)$ $22$

Sum of $n$ terms of series $12 + 16 + 24 + 40 + .....$ will be

The set $A = \{ x:x \in R,\,{x^2} = 16$ and $2x = 6\} $ equals

The straight lines $x + 2y - 9 = 0,$ $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, if the straight line $35x - 22y + 1 = 0$ passes through the point