How do you do this question?

Step-by-step explanation:

f(x) = sin(x), a = π/6, n = 4

Find the derivatives.

f⁽⁰⁾(π/6) = sin(π/6) = ½

f⁽¹⁾(π/6) = cos(π/6) = ½√3

f⁽²⁾(π/6) = -sin(π/6) = -½

f⁽³⁾(π/6) = -cos(π/6) = -½√3

f⁽⁴⁾(π/6) = sin(π/6) = ½

T₄(x) = ½ (x − π/6)⁰ / 0! + ½√3 (x − π/6)¹ / 1! − ½ (x − π/6)² / 2! − ½√3 (x − π/6)³ / 3! + ½ (x − π/6)⁴ / 4!

T₄(x) = ½ + ½√3 (x − π/6) − ¼ (x − π/6)² − ¹/₁₂√3 (x − π/6)³ + ¹/₄₈ (x − π/6)⁴

Find the fifth derivative.

f⁽⁵⁾(x) = cos(x)

So the next term of the series would be:

cos(z) (x − π/6)⁵ / 5!

For 0 ≤ z ≤ π/3,│f⁽⁵⁾(x)│is a maximum at z = 0.  Therefore:

│R₄(x)│≤ │cos(0) (0 − π/6)⁵ / 5!│

│R₄(x)│≤ 0.000328

│R₄(x)│is always positive, so we can ignore the bottom two graphs.  The top right graph has a y-intercept of approximately 0.0003, so that is the correct graph.

step-by-step explanation:

idk

step-by-step explanation:

i don't know