If f(x)=⎧⎨⎩sin[x][x],[x]≠00,[x]=0, where [x] denotes the greatest integer less than or equal to x then limx→0f(x) equals
A
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
does not exist
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D does not exist The given function can be restated as f(x)=⎧⎨⎩sin[x][x]ifxϵ(−∞,0)∪[1,∞]0ifxϵ[0,1) ∴limx→0−f(x)=limh→0sin[−h][−h] =limh→0sin(−1)(−1)=sin1andlimx→0+f(x)=limh→00=0 ∵limx→0+f(x)≠limx→0+f(x) ∴limx→0f(x) does not exist