Suppose the functions f(x) and g(x) are defined for all x and that lim_{xrightarrow0}f(x)=frac{1}{2} and lim_{xrightarrow0}g(x)=sqrt2. Find the limits as xrightarrow0 of the following functions. f(x)frac{cos x}{x-1}

nitraiddQ 2021-01-15 Answered
Suppose the functions f(x) and g(x) are defined for all x and that limx0f(x)=12 and limx0g(x)=2. Find the limits as x0 of the following functions. f(x)cosxx1
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Expert Answer

gotovub
Answered 2021-01-16 Author has 98 answers
Given
limx0f(x)=12 and limg(x)=2
we have to find
f(x)cosxx1
we know
limx0f(x)g(x)=[limx0f(x)][limx0g(x)]
and limx0f(x)g(x)=limx0f(x)limx0g(x)
limx0f(x)cosxx1=[limx0f(x)][limx0cosxx1]
=12limx0cosxlimx0(x1)
=1211
=12
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