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Generalizing to an arbitrary function.  TOPIC_SOLVED

\mbox{Exercise 1A-4: \mbox{a) Show that every polynomial is the sum of} \mbox{an even and an odd function.} \mbox{b) Generalize part (a) to an arbitrary function }\, f(x) \mbox{by writing} f(x)\, =\, \frac{f(x)\, +\, f(-x)}{2}\, +\, \frac{f(x)...
by sepoto
on Fri Oct 25, 2013 10:57 pm
 
Forum: Calculus
Topic: Generalizing to an arbitrary function.
Replies: 1
Views: 726

Finding all tangent lines through the origin.  TOPIC_SOLVED

\mbox{Question 1C-5:} . . . \mbox{Find all tangent lines through the origin} . . . \mbox{to the graph of }\, y\, =\, 1\, +\, (x\, -\, 1)^2 \mbox{Solution 1C-5:} \mbox{Method 1: }\, y'(x)\, =\, 2(x\, -\, 1),\, \mbox{ so the tangent line through} (a,\, 1\, +\, (a\,...
by sepoto
on Tue Oct 29, 2013 5:36 am
 
Forum: Calculus
Topic: Finding all tangent lines through the origin.
Replies: 1
Views: 806

Discontinuity and inequalities.  TOPIC_SOLVED

Question 1D-5: Define f(x)\, =\, \begin{cases}ax\, +\, b,&x\, \ge\, 1\\x^2&x\, <\, 1\end{cases} a) Find all values of a and b such that f(x) is continuous. b) Find all values of a and b such that f'(x) is continuous. (Be careful!) Solution 1D-5: a) For continuity,...
by sepoto
on Thu Oct 31, 2013 4:34 am
 
Forum: Calculus
Topic: Discontinuity and inequalities.
Replies: 1
Views: 888

Differential Equations.  TOPIC_SOLVED

I am studying differential equations and I have a question about whats in my lecture notes. Here is a link to the lecture notes: http://sdrv.ms/1gYECTo a) (\frac{d}{dx}+x)y=0 -------------- b) (\frac{dy}{dx}+xy)=0 In the first equation above a) I am trying to get a handle on what is ...
by sepoto
on Wed Dec 11, 2013 7:06 am
 
Forum: Calculus
Topic: Differential Equations.
Replies: 1
Views: 549

Uniqueness of an Anti Derivative up to a Constant.  TOPIC_SOLVED

http://sdrv.ms/1dgPhG8 If F'(x) = f(x), and G'(x) = f(x), then G(x)=F(x)+c for some constant c Proof: (G-F)'=f-f=0 Recall that we proved as a corollary of the Mean Value Theorem that if a function has a derivative zero the it is constant. Hence G(x)-F(x) = c ( for some constant c). That is, G(x)=F(x...
by sepoto
on Mon Dec 16, 2013 6:49 am
 
Forum: Calculus
Topic: Uniqueness of an Anti Derivative up to a Constant.
Replies: 1
Views: 592

Integration: int ( x / sqrt[8-2x^2] ) dx  TOPIC_SOLVED

http://sdrv.ms/19P0FGN
http://sdrv.ms/19P0Gun

In regards to:





So the solutions manual says:


I'm wondering is that a typo? Is it not supposed to be:


Thank You...
by sepoto
on Tue Dec 17, 2013 6:47 am
 
Forum: Calculus
Topic: Integration: int ( x / sqrt[8-2x^2] ) dx
Replies: 1
Views: 594

Defenite Integral. Change of Variables.  TOPIC_SOLVED

https://public.dm2301.livefilestore.com/y2pBn4vfEskRcdIQBjTpMk_SkebEAHsQKxF7pgIhvYNlheRH6TSPx4503rgjSXzBKZDMQnSjnmLtNvb2PzbeY-8PWng30rXSi2jSWBRo7F1sAE/3e2q.PNG?psid=1 https://public.dm2303.livefilestore.com/y2p0g1L09CyEmds-W3ti1-7_vWmmwPCENdJ40sycm8-fvIrKFMgqaI1M0QUVo5ToiSQIn2_87dai8a2-6x-a6LSVXxzS...
by sepoto
on Mon Dec 23, 2013 7:13 am
 
Forum: Calculus
Topic: Defenite Integral. Change of Variables.
Replies: 3
Views: 859

Re: Defenite Integral. Change of Variables.  TOPIC_SOLVED

The limit as x approaches infinity of the definite integral below (I hope I have the right definite integral, there are two others to choose from in this problem): \frac{1}{\sqrt{\pi}}\int^{x/\sqrt{2}}_{0}e^{-t^{2}}dt My solutions manual shows the result of the calculation to be: \lim(x \to \inf...
by sepoto
on Mon Dec 23, 2013 9:39 pm
 
Forum: Calculus
Topic: Defenite Integral. Change of Variables.
Replies: 3
Views: 859

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