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Question: Answered & Verified by Expert
If $f(x)= \begin{cases}\frac{\cos a x-\cos b x}{x^2}, & x \neq 0 \\ \frac{1}{2}\left(a^2-b^2\right) & , x=0\end{cases}$
where $a, b$ are real and district constants, then
MathematicsContinuity and DifferentiabilityAP EAMCETAP EAMCET 2017 (24 Apr Shift 2)
Options:
  • A $f$ is discontinuous at $x=0$
  • B $f$ is continuous at $x=0$
  • C $\lim _{x \rightarrow 0} f(x)$ does not exist
  • D $f(0)$ is not defined
Solution:
2862 Upvotes Verified Answer
The correct answer is: $f$ is discontinuous at $x=0$
No solution. Refer to answer key.

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