Register to reply

Question about Taylor series and implicit function theorem.

by furi0n
Tags: function, implicit, series, taylor, theorem
Share this thread:
furi0n
#1
Jan10-12, 03:24 PM
P: 20
Hi everyone,
i'll have final exam next week, and have a problem on sheet given by prof.
i attached question as a picture...
respectively,
the first question of sheet is about taylor series as you can see, although we haven't learn about taylor series on two variables, maybe he asked for us to search about this question. do you have any idea (probably have :D ), may you give me hint or same way to solve first question...

In the fifth question, i used implicit functn thrm, i define F(x,y,u,v)=T(x,y)-(u,v)=0, and i found d(u,v)/d(x,y) and d(x,y)/d(u,v). find answer is zero but it should have been zero where do i mistake, is there other choice different from implicit fnctn thrm, then i can understand my mstake or may you help to find my mistake...


in second picture, last question, how can i show the function f has a local min at (0,0) on the line through (0,0). i am considered y=mx line equation as a side condition but this shows me only that (0,0) is a critical point. It's the point i am confused.


thank you for your interest.
Attached Thumbnails
Photo0377[1].jpg   Photo0378[1].jpg  
Phys.Org News Partner Science news on Phys.org
Suddenly, the sun is eerily quiet: Where did the sunspots go?
'Moral victories' might spare you from losing again
Mammoth and mastodon behavior was less roam, more stay at home

Register to reply

Related Discussions
Implicit Function Theorem Question! Calculus 5
Implicit Function Theorem Calculus & Beyond Homework 1
Implicit Function Theorem Calculus & Beyond Homework 0
Implicit function theorem Calculus & Beyond Homework 0
Question about implicit function theorem Calculus & Beyond Homework 3