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1-lim-x-0-sin-1-x-2-lim-x-sin-x-




Question Number 58867 by malwaan last updated on 01/May/19
1:  lim_(x→0)  sin((1/x))  2: lim_(x→∞)  sin(x)
1:limx0sin(1x)2:limxsin(x)
Commented by tanmay last updated on 01/May/19
1)lim_(x→0)  sin((1/x))   the limiting value lies between ±1  2) t=(1/x) when x→∞  t→0  lim_(t→0)  sin((1/t))  the limiting value lies between ±1  attaching graph for clarity.
1)limx0sin(1x)thelimitingvalueliesbetween±12)t=1xwhenxt0limt0sin(1t)thelimitingvalueliesbetween±1attachinggraphforclarity.
Commented by tanmay last updated on 01/May/19
Commented by tanmay last updated on 01/May/19
Commented by malwaan last updated on 01/May/19
lim_(x→0^+ )  sin((1/x))→+ve  lim_(x→0^− )  sin((1/x))→−ve  ∴ lim_(x→0)  sin((1/x)) does not exist  Am I right ?  please check ....
limx0+sin(1x)+velimx0sin(1x)velimx0sin(1x)doesnotexistAmIright?pleasecheck.

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