Math  /  Calculus

Question Calculate the 2nd and 3rd order Taylor polynomials for f(x)=8tan(x)f(x) = 8 \tan(x) centered at a=0a = 0. Express the polynomials using symbolic notation and fractions.

Studdy Solution
Further simplify T3(x)T_{3}(x) by reducing the fraction.
T3(x)=8x+83x3 T_{3}(x) = 8x + \frac{8}{3}x^3
The Taylor polynomials centered at a=0a=0 for the function f(x)=8tan(x)f(x)=8 \tan (x) are: T2(x)=8x T_{2}(x)= 8x T3(x)=8x+83x3 T_{3}(x)= 8x + \frac{8}{3}x^3

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