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

If the function f(x)=⎪ ⎪⎪ ⎪x+a22sin x,0x<π4x cot x+b,π4x<π2b sin 2xa cos 2x,π2xπ is continuous in the interval [0,π] , then the values of (a,b) are

A
(–1, –1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(0,0)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(–1, 1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(1,-1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B (0,0)


since f is continuous at x = π4

f(π4)fh0(π4+h)fh0(π4h)

π4cotπ4+bfh0(π4+h)+a22sin(π4+h)

π4(1)+b(π4+0)+a22 sin(π4+0)

π4+bπ4+a22 sinπ4

ba2212ba2

Also as f is continuous at x - π4

f(π2)=limxπ20f(x)=limx0f(π2h)

b sin 2π2a cos 2π2=limh0[(π2h)cot(π2h)+b]

b.0a(1)=0+ba=b

Hence (0,0) satisfy the above relations.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Continuity in an Interval
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon