Calculus Answers

1. What is the maximum error possible in using the Taylor polynomial approximation

sin(x)≈x-((x^3)/3!)+((x^5)/5!) when -0.3≤x≤0.3?. Use this approximation to find sin(12^0) correct to six decimal places. (Note that 12^0=12π/180).

1. Integrate the function f(x,y)=6x+(2y^2) over the region R bounded by the parabola x=y^2 and the straight line x+y=2.

Find the derivative f m(x) of the following function with respect to x:

fm(x) = ( m

X * n^ x · x ^n )^2

n=1

Find the derivative f 0 m(x) of the following function with respect to x: fm(x) = Xm n=1 n x · x n !2

A painting in an art gallery has height 3 m and is hung so that its lower edge is about 1 m above the eye of an observer. How far from the wall should the observer stand to get the best view? (i.e. the observer wants to maximize the angel θ subtended at the eye by the painting