Determine whether the statement is true or false. Explain your answer. If p 6 ( x ) is the sixth-degree Taylor polynomial for function f about x = x 0 , then p 6 ( 4 ) ( x 0 ) = 4 ! f ( 4 ) ( x 0 ) .
Determine whether the statement is true or false. Explain your answer. If p 6 ( x ) is the sixth-degree Taylor polynomial for function f about x = x 0 , then p 6 ( 4 ) ( x 0 ) = 4 ! f ( 4 ) ( x 0 ) .
Consider f (x) = 2x* – x3 – 5x2 + 2x + 2.
1. List all possible zeros (candidates) for f(x).
2.
Define f (x) in your calculator or desmos. Use the graph to narrow down your candidates.
Use synthetic division to reduce f (x) to a quadratic expression. Factor the resulting
quadratic expression to find the last two zeros.
ZEROS:
3. Express f(x) as a product of linear factors. Don't forget to include the value of a!
Find the nth Maclaurin polynomial for the function.
The upward velocity of a rocket is given as a function of time in Table 1.
Table 1. Velocity as a function of time.
t (s)
v(t) (m/s)
10
227.04
15
362.78
20
517.35
22.5
602.97
30
901.67
Using a second order polynomial interpolant for velocity and find the velocity of the rocket at
t=16 seconds.
Chapter 9 Solutions
Calculus Early Transcendentals, Binder Ready Version
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