Question #223819

limz→0 z^{2}-sinz/z


1
Expert's answer
2021-08-11T07:28:40-0400

limz0(z2sin(z)z)limxa[f(x)±g(x)]=limxaf(x)±limxag(x)Withtheexceptionofindeterminateform=limz0(z2)limz0(sin(z)z)=01=1\lim _{z\to \:0}\left(z^2-\frac{\sin \left(z\right)}{z}\right)\\ \lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\ With\:the\:exception\:of\:indeterminate\:form\\ =\lim _{z\to \:0}\left(z^2\right)-\lim _{z\to \:0}\left(\frac{\sin \left(z\right)}{z}\right)\\ =0-1\\ =-1


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