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November 29th, 2014, 02:34 PM   #1
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Fundamental Theorem

How do I approach these problems? I only know how to solve C.
Attached Images 20141129_173005.jpg (88.2 KB, 9 views) November 29th, 2014, 03:00 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 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, 03:35 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 04:18 PM. November 29th, 2014, 04:25 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, 06:17 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, 11:06 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, 07:16 AM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra You need to say what d) tells you about $N(x)$. Tags fundamental, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Omnipotent Calculus 1 November 27th, 2014 02:11 PM Mr Davis 97 Calculus 6 June 5th, 2014 03:29 PM ray Algebra 6 April 22nd, 2012 04:50 AM Aurica Calculus 1 June 14th, 2009 09:04 AM Aurica Calculus 1 June 10th, 2009 06:39 PM

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