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Differential Calculus

Scorching goIITian

Joined:	25 Feb 2007
Post:	225

26 Feb 2007 02:53:28 IST

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610

requiring tricks...

None

lim sin x

---------- =????

1/x->0 x

i have solved by sandwich theorem,hoping to get any other process.

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atif alam

Cool goIITian

Joined: 14 Feb 2007

Posts: 33

26 Feb 2007 03:08:27 IST

Like 2 people liked this

it is not as difficult as u taking it

replace 1/x by t

_{[t ]}

_{[ 0]} t sin(1/t)

as t tends to 0, 1/t tends to infinty but sin(1/t) is any real no. lying b/w -1 &+1

so the answer is simply 0

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

26 Feb 2007 18:45:24 IST

Like 0 people liked this

Let 1/x = z

Then limit becomes

_[z]

_[0] z.sin(1/z)

Now sin(1/z) is an oscillating function whose values lies between -1 and 1.

Hence as z tends to 0 the limit also becomes zero.

Hence the answer is 0.

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