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Limits Continuity and Differentiability question

2021 · 22 Jul · Shift 2 · Q36
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  5. /2021 · 22 Jul · Shift 2 · Q36

Limits Continuity and Differentiability question

2021 · 22 Jul · Shift 2 · Q36

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1
Let f : R →\to→ R be defined as f(x)={x3(1−cos⁡2x)2log⁡e(1+2xe−2x(1−xe−x)2),xe0α,x=0f(x) = \left\{ {\begin{matrix} {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{1 + 2x{e^{ - 2x}}} \over {{{(1 - x{e^{ - x}})}^2}}}} \right),} & {x e 0} \\ {\alpha ,} & {x = 0} \\ \end{matrix} } \right.f(x)={(1−cos2x)2x3​loge​((1−xe−x)21+2xe−2x​),α,​xe0x=0​ If f is continuous at x = 0, then α\alphaα is equal to :
  1. A
    1
  2. B
    3
  3. C
    0
  4. D
    2
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