IIT JEE , AIEEE Forum - Mathematics , Differential Calculus - Lt x--0 sin{x}/{x} { }-fractional part of x ans-sin 1

sweet08

Lt x--0 sin{x}/{x} { }-fractional part of x ans-sin 1

hash_include

limit doesn't exist..
LHL is lim x-->0- sin{x}/{x} = sin1 [ as {x} --> 1 as x ---> 0 ]

RHL is lim x ---> 0+ sin{x}/{x} = 1

EDIT: sorry.. didnt realize there was another thread for this

RyuAmakusa

f(x) = sin{x}/{x} = sin( x - [x])/x-[x]

_{[x ]}

_[0]--f(x) = _{[ h]}

_{[ 0]}f(-h) = _{[ h][ 0]}sin(-h -(-1))/-h+1 = sin1

_{[x ][0]+}f(x) = _{[ h]}

_{[ 0]}f(h) =_{[ h][ 0]}sin(-h -(0))/-h-0 = 1

I think lim does not exist plz. correct if wrong

eistien

limit does not exist

obviously

LHL is lim x-->0- sin{x}/{x} = sin1

RHL is lim x ---> 0+ sin{x}/{x} = 1

i think you must have considered only the LHL check out!!!!

sweet08

sorry it is x--->0^-

limit doesnt exist

rhl is sin 1

sweet08

sorry LHL is sin 1

computer001

RHL is 1
LHL is sin1..
thts wats written in prev post also...

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