November 29th, 2014, 02:34 PM  #1 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4  Fundamental Theorem
How do I approach these problems? I only know how to solve C.

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 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4  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 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677  
November 29th, 2014, 06:17 PM  #5  
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4  Quote:
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  
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244  Quote:
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 $N(x)$.


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