Find the taylor series about 0 for each of the functions below. give the first three non-zero terms for each.

a. x2sin(x2)−x4= + + +⋯

b. 2cos(x)+x2= + + +⋯ for each of these series, also be sure that you can find the general term in the series!

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12

Amodel rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y = -0.04x^2 + 8.6x + 4.8, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. how far horizontally from its starting point will the rocket land? a. 0.56 m b. 215.56 m c. 431.11 m d. 215.74 m

Which equation is y = -6x2 + 3x + 2 rewritten in vertex form?