JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \( f(x)=\left\{\begin{array}{cc} \frac{a|x|+x^2-2(\sin |x|)(\cos |x|)}{x} & , x \neq 0 \\ b & , x=0 \end{array}\right. \) is continuous at \( x=0 \) then \( a+b \) is equal to:
- A 1
- B 2
- C 0
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}\frac{a|x|+x^2-2 \sin |x| \cos |x|}{x} & ; x \neq 0 \\ b & ; x=0\end{array}\right.\) for continuity \(\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x)=f(0)\) \(\lim _{x \rightarrow 0^{-}} \frac{ ah + h ^2-2(\sinh ) \cosh }{- h }\)…
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