JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q7

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MathematicsSingle correct+4 / -1Question 7 of 90

If the function $f(x)=\begin{cases}\dfrac{\log_e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, & x\in\left(\dfrac{-\pi}2,\dfrac\pi2\right)-\{0\}\\ k, & x=0\end{cases}$ is continuous at $x=0$ , then k is equal to :

-1

Answer and worked solution

Official answer: A

Numerator $\ln(1+x^2+x^4)\sim x^2$ ; denominator $\frac{\sin^2x}{\cos x}\sim x^2$ . Limit 1.

(A)

Topics:Continuity Limits

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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 7