Question

f(x) =2x and ga(x) =1/3x
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Answer 1

Answer:

If f(x)=cot−1(3x−x31−3x2) and g(x)=cos−1(1−x21+x2) then limx→af(x)−f(a)g(x)−g(a)

Step-by-step explanation:

tanθ=a

0<tanθ<12

0<θ<π6

x=tanθ

f(x)=cot−1(tan3θ)=π2−tan−1tan3θ

=π2−3θ

g(x)=cos−1cos2θ=2θ

limx→af(x)⋅f(a)g(x)⋅g(a)⋅x−ax−a=f'(a)g'(a)

f(x)=π2−3tan−1x

diff. with respect to x

f'(x)=0−31+x2

g(x)=2tan−1x

diff. with respect to x

g'(x)=21+x2

f'(a)g'(a)=−31+a3⋅1+a22=−32