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November 29th, 2014, 01:34 PM   #1
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Fundamental Theorem

How do I approach these problems? I only know how to solve C.
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 November 29th, 2014, 02:00 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 2,980 Thanks: 1574 if u is a function of x and a is a constant ... $\displaystyle \frac{d}{dx} \int_a^u f(t) \, dt = f(u) \cdot \frac{du}{dx}$
November 29th, 2014, 02:35 PM   #3
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Quote:
 Originally Posted by skeeter if u is a function of x and a is a constant ... $\displaystyle \frac{d}{dx} \int_a^u f(t) \, dt = f(u) \cdot \frac{du}{dx}$
so for #a I can describe the region as f(x) = e^(-a^2 / 2) right?

Last edited by Omnipotent; November 29th, 2014 at 03:18 PM.

November 29th, 2014, 03:25 PM   #4
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Quote:
 Originally Posted by Omnipotent so for #a I can describe the region as f(x) = e^(-a^2 / 2) right?
no ... the region is the signed area under the curve $\displaystyle y = e^{-x^2/2}$ and above the x-axis from x = 0 to x = a

maybe you should look at the graph of the function.

November 29th, 2014, 05:17 PM   #5
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Quote:
 Originally Posted by skeeter no ... the region is the signed area under the curve $\displaystyle y = e^{-x^2/2}$ and above the x-axis from x = 0 to x = a maybe you should look at the graph of the function.
Thank you. I'm sorry to bother you again but could you tell me if this is correct?

b) N(0) = 0 because 0 is the start of the interval

c) n'(x) = e^(-x^2 / 2)

n''(x) = -4x*e^(-x^2 / 2)

d) lim as x approaches infinity = 0

November 29th, 2014, 10:06 PM   #6
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Quote:
 Originally Posted by Omnipotent Thank you. I'm sorry to bother you again but could you tell me if this is correct? b) N(0) = 0 because 0 is the start of the interval c) n'(x) = e^(-x^2 / 2) n''(x) = -4x*e^(-x^2 / 2) d) lim as x approaches infinity = 0
b) is correct.

Check your answer for $N''(x)$. Remember$$\dfrac{d}{dx}\left(e^{-x^2/2}\right) = e^{-x^2/2}.\dfrac{d}{dx}\left(\dfrac{-x^2}{2}\right)$$

d) is also correct.

 November 30th, 2014, 06:16 AM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra You need to say what d) tells you about $N(x)$.

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