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Wed 13 Nov, 2013 06:48 pm
1) What constant acceleration is required to increase the speed of a car from 26 mi/h to 53 mi/h in 2 s?
2) Find f.
f '''(x) = cos x, f(0) = 3, f '(0) = 1, f ''(0) = 9
3)Find the most general antiderivative of the function.
f(x) = (x + 5)(5x − 10)
I am struggling with these in particular, if someone would be so kind to show how the answer is found that would be great, thanks!
@mjborowsky,
mjborowsky wrote:
1) What constant acceleration is required to increase the speed of a car from 26 mi/h to 53 mi/h in 2 s?
I'll get you started.
That's 27 mi/hr in 2 s.
You didn't state the units in which you want the final answer, so I'll assume ft/sec.
27 mi/hr = 27 mi/hr x (5280 ft/1 mi) x (1 hr/3600 s) = (27 x 5280)/3600 ft/sec
= 39.6 ft/sec
To gain this speed in 2 s requires an acceleration of (29.6 ft/s) / (2 s) = 19.8 ft/s^2 (feet per second squared)
@mjborowsky,
mjborowsky wrote:
2) Find f.
f '''(x) = cos x, f(0) = 3, f '(0) = 1, f ''(0) = 9
f'' = sin x + C
f' = - cos x + Cx + D
f = - sin x + (Cx^2)/2 + Dx + E
f(0) = E = 3
f'(0) = -1 + D = 1
D = 2
f''(0) = C = 9
So, f = - sin x + (9/2) x^2 + 2x + 3
@mjborowsky,
mjborowsky wrote:
3)Find the most general antiderivative of the function.
f(x) = (x + 5)(5x − 10)
Using the FOIL method, multiply it out.
f(x) = 5x^2 - 10x + 25x - 50
= 5x^2 + 15x - 50
The antiderivative (or indefinite integral) is:
(5/3) x^3 + (15/2) x^2 - 50x + C
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