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flimt0 sin2 t

Question

How do I find this limit?

 

 

f
lim
t0 sin2 t
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f lim t0 sin2 t

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Step 1

Here, since limit of numerator and denominator is 0 as t approaches 0, so , we use L'hospital's rule as shown on board.

lim
limsin2t = 0
t0
t0
2t
2t
- lim
t0 sin 2
lim dt
t0 d
lim
t 0 sin t
- lim
t0 2sint cos t
(sin t)
dt
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lim limsin2t = 0 t0 t0 2t 2t - lim t0 sin 2 lim dt t0 d lim t 0 sin t - lim t0 2sint cos t (sin t) dt

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Step 2

Again,e use L'hospital's rul...

(21)
2
2
lim-
t0 2 cos 2t
2t
= lim
t0 sin 2t
dt
lim
t0 d
1
2 cos 0
lim
t0 şint
sin 2t)
dt
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(21) 2 2 lim- t0 2 cos 2t 2t = lim t0 sin 2t dt lim t0 d 1 2 cos 0 lim t0 şint sin 2t) dt

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Tagged in

Math

Calculus

Limits

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