If f (x )=( a |x |+x^2-2 ( sin |x | ) ( cos |x | )x ,x 0b ,x=0) is continuous at x=0, then a+b is equal to

Question

Accepted Answer

Correct answer: C. (c) Note 2 sin (x ) cos |x |= sin ⁡ (2 |x | ). For x>0 : f (x )=a+x- sin2xx x 0^+ a-2. For x<0 :f (x )=-a+x+ sin2xx x 0^- -a+2. For continuity: a-2=2-a ⇒a=2, and b=a-2=0. a+b=2.

$If f (x) = (\frac{a | x | + x ^{2} - 2 ( sin | x | ) ( cos | x | )}{x}, x \neq = 0 b, x = 0) is continuous at x = 0, then a + b is equal to$

Solution

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