1. Let P(x)=3x^2-5x^3+7x^4+3x^5 be the fifth-degree Taylor polynomial for the function f about x=0.What is the

Question

value of f'''(0)?
2. Insects destroyed a crop at the rate of (100e^-0.1t)/(2-e^-3t) tons per day, where time t is measured in days. To the nearest ton, how many tons did the insects destroy during the time interval 7≤t≤14?
3. A particle moves in the xy-plane so that its position at any time t is given by x(t)=t^2 and y(t)=sin(4t). What is the speed of the particle when t=3?

Answer 1

1. The third-order term is f'''(0).x^3/3! = -5x^3, so f'''(0) = -5(3!) = -30.

2. For t ≥ 7, e^(-3t) ≤ 7.6×10^-10 which is negligible in comparison to 2, so start with
L = ∫(7 to 14) (100e^(-0.1t)) / 2 dt
The correct value will be within less than 1 part in 10^9 of this integral.
= [50 e^(-0.1t) / (-0.1)] [7 to 14]
= -5(e^(-1.4) - e^(-0.7))
= 1.25 to 2 d.p.
So the error in L is not going to affect the result to the nearest ton, which is 1 ton.

3. dx/dt = 2t, dy/dt = 4 cos 4t. At t = 3 we have dx/dt = 6, dy/dt = 4 cos 12. So the speed is √(6^2 + 16 cos^2 12) = 6.88 to 2 d.p.

Answer 2

in spite of is interior the bracket is what you're anticipated to replace into your function. on the 2nd the function is labelled f(x), and so in case you notice all your constants are x. with the intention to end those questions, while given a query the place f(n) you in basic terms replace your x values with this and total up the scores. F(x) = -4x^4 + 2x^2 - a million So f(-a million) = -4 x -a million^4 + 2 x -a million^2 -a million = -4 x a million + 2x1- a million = -4+2-a million = -3 f(2) = -4 x 2^4 +2x2^2-a million = -4x16+2x4-a million = -sixty 4 +8-a million = -fifty six-a million = -fifty seven