1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Let f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩−2sinxifx≤−π2Asinx+Bif−π2<x<π2;cosxifx≥π2For what values of A and B, the function f(x) is continuous throughout real line?

A
A=1,B=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
A=1,B=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
A=1,B=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
A=1,B=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C A=−1,B=1Givenf(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩−2sinxifx≤−π2Asinx+Bif−π2<x<π2;cosxifx≥π2From above conditions function f(x) is continuous throughout the real line, when function f(x) is continuous at x=−π2 and π2For continuity at x=−π2limx→π−2f(x)=limx→π+2f(x)=f(−π2)...(ii)limx→π−2f(x)=2limx→π+2f(x)=−A+Bf(−π2)=2∴ From Eq (ii) we get−A+B=2....(iii)For continuity at x=π2limx→π−2f(x)=limx→π+2f(x)=f(π2)...(iv)Here limx→π−2f(x)=A+B⇒limx→π+2f(x)=0And f(π2)=0∴ from Eq(iv)A+B=0....(v)From Eqs. (iii) and (iv)A=−1,B=1

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Algebra of Continuous Functions
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program