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Mathematics · 2022

JEE Main · 30 July 2022, Shift 2 · Q69

Let f(x)= {(sin (a x+3 x)+ sin x)/x, x<0; 2, x=0; ((x+6 b x^2)^(1/3)-x^(1/3))/(3 x^4 / 3), x>0} be continuous at x=0. If (1-k) f(7/18)=a b, then k is…

Let $$f(x)=\left\{\begin{array}{cc} \frac{\sin (a x+3 x)+\sin x}{x}, & x<0 \\ 2, & x=0 \\ \frac{\left(x+6 b x^2\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{3 x^{4 / 3}}, & x>0 \end{array}\right. $$ be continuous at $\displaystyle x=0$. If $\displaystyle (1-k) f\left(\frac{7}{18}\right)=a b$, then $\displaystyle k$ is equal to
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.