Limits involving transcendental functions. Analyze the following limits after de

Bevan Mcdonald

Bevan Mcdonald

Answered question

2021-10-31

Limits involving transcendental functions. Analyze the following limits after determining the continuity of the functions involved.
limx0cos2x1cosx1

Answer & Explanation

Luvottoq

Luvottoq

Skilled2021-11-01Added 95 answers

To determine:
The limit of the given function after determining the continuity of the function.
limx0cos2x1cosx1
Explanation:
The function f(x) is continuous when the right- hand limit and the left -hand limit and the function value at the given point is the same.
f(x)=cos2x1cosx1
For the left-hand limit, x approaches 0 from the left side.
limx0f(x)=limx0cos2(x)1cos(x)1
limx0cos2(x)1cos(x)1=limx0(cos(x)1)(cos(x)+1)cos(x)1
limx0f(x)=limx0cos(x)+1=cos(0)+1
limx0f(x)=1+1=2
Now the right-hand limit is,
limx0+f(x)=limx0+cos2(x)1cos(x)1
limx0+cos2(x)1cos(x)1=limx0+(cos(x)1)(cos(x)+1)cos(x)1
limx0+f(x)=limx0+cos(x)+1=cos(0)+1
limx0+=1+1=2
Also, the function value at x=2 is,
f(0)=cos2(0)1cos(0)1=cos
Jeffrey Jordon

Jeffrey Jordon

Expert2022-06-24Added 2605 answers

Answer is given below (on video)

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