Find the linearization L(x) of the function at a. f(x)=\sin x, a= \frac{\pi}

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-09-11

Find the linearization L(x) of the function at a. f(x)=sinx,a=π6

Answer & Explanation

unessodopunsep

unessodopunsep

Skilled2021-09-12Added 105 answers

Linear approximation of (fx) at x=a is  
L(x)=f(a)+f(a)(xa)
Therefore  
Linear approximation of  f(x)  at  x=π6  is
L(x)=f(π6)+f(π6)(xπ6)
f(x)=sinxf(π6)=sin(π6)=12
f(x)=cosxf(π6)=cos(π6)=32
Therefore
L(x)=12+32(xπ6)

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