If f(x) = { `sin[x] /[x],[x] != 0 ; 0, [x] = 0}` , Where[.] denotes th – InterviewSolution

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1.	If f(x) = { `sin[x] /[x],[x] != 0 ; 0, [x] = 0}` , Where[.] denotes the greatest integer function, then `lim_(x rarr 0) f(x)` is equal toA. 1B. 0C. `-1`D. Does not exist
Answer» Correct Answer - d Given, `f(x) = {{:(sin[x]/[x]",",[x]ne0), (0,[x]=0):},` `therefore` LHL = `lim_(xto0^(-))(sin[x])/([x])=lim(xto0)(sin[0-h])/([0-h])` `=lim_(hto0)(-sin[-h])/([-h]) =-1` RHL `=lim_(xto0)f(x) = lim_(xto0^(+))(sin[x])/([x])` `=lim_(xto0^(+)) (sin[0+h])/([0+h])=lim_(hto0)(sin[h])/([h])=1` `therefore LHL ne RHL` So, limit does not exist.

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