wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The values of a and b so that the functionf(x)= ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪x+a2sinx,0x<π42xcotx+b,π4xπ2acos2xbsinx,π2<xπ is continuous at x=π4,π2 are

A
a=π6
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a=π6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
b=π12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
b=π
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C b=π12
f(x) is continuous in the interval 0x<π4,π4<x<π2,π2<xπ
We need to make the function continuous at x=π4,π2
For continuity at x=π4,limxπ4f(x)=limxπ4+f(x)=f(π4)
limx(π4)(x+a2sinx)=limx(π4)+(2xcotx+b)=f(π4)
π4+a2sin(π4)=2.π4.cot(π4)+b=2π4.cot(π4)+b
π4+a=π2+bab=π4 ...(1)
For continuity at x=π2,limxπ2f(x)=limxπ2+f(x)=f(π2)
limxπ2(2xcotx+b)=limx(π2)+(acos2xbsinx)=acosπbsinπ2
0+b=aba+2b=0 ...(2)
From equation (1) and (2)
a=π6,b=π12

flag
Suggest Corrections
thumbs-up
31
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon