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Fx =cosecx-2/root3 divided by tanx- root3 for fx is continous at pie /3?
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Fx =cosecx-2/root3 divided by tanx- root3 for fx is continous at pie /...
When you put π/3 as limit in eq. then we get 0/0 indeterminant form...so in case u can apply Lhopitals rule ..ie, differentiate numerator and denomination separately and put direct limit..but remember before applying Lhopitals be aware that function must be continuous (here tan and cosec are always continuous in their domain)..
sol. {cosecx - 2/√3}/{tanx - √3}
applying Lhopitals.. ddx{cosecx - 2/√3}/ddx{tanx - √3}
={-cosecxcotx - 0}/{sec²x - 0}
(now indeterminant form has gone, u can directly put limit as x= π/3)
on putting u get ans = -8/3
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Fx =cosecx-2/root3 divided by tanx- root3 for fx is continous at pie /3?
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