Note 2sin∣x∣cos∣x∣=sin(2∣x∣).
For x>0: f(x)=a+x−xsin2xx→0+a−2.
For x<0: f(x)=−a+x+xsin2xx→0−−a+2.
For continuity: a−2=2−a⇒a=2, and b=a−2=0.
a+b=2.
If f(x)={xa∣x∣+x2−2(sin∣x∣)(cos∣x∣)b,x=0,x=0
is continuous at x=0, then a+b is equal to
Held on 23 Jan 2026 · Verified 6 Jul 2026.
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