Let f : R³ → R be de?ned by:
                                       f(x, y, z) = xy²+ x³z⁴+ y⁵z⁶

a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) .

b) Brie?y explain why f must be a di?erentiable function (you just need to "look" at the equations for the partial derivatives).

c) Find D~uf(2, 1, 1) where ~u is a unit vector in the direction of ~v = h4, 3,-1i .

d) Find an equation for the plane which is tangent to the surface de?ned by

xy²+ x³z⁴+ y⁵z⁶= 11

 at the point (2, 1, 1) .

e) Use di?erentials to approximate the value of f(2.01, 1.02, 0.97) . Use a calculator to
?nd a more accurate value, and compare.

Posted Date: 3/14/2013 5:26:47 AM | Location : United States

Ask an Expert

Related Discussions:- Explain why f must be a di?erentiable function, Assignment Help, Ask Question on Explain why f must be a di?erentiable function, Get Answer, Expert's Help, Explain why f must be a di?erentiable function Discussions

Write discussion on Explain why f must be a di?erentiable function
Your posts are moderated

Write your message here..

Related Questions

Find the co ordinates of p such that ap =3/7 ab and p lies, If A & B are (-... If A & B are (-2,-2) and (2,-4) respectively, find the co ordinates of P such that AP =3/7 AB and P lies on the line segment AB.

Find the are length and sketch the level curves, 1) Find the are length of ... 1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2

Three whole divisions, In the National Hockey championship, there are 30 in... In the National Hockey championship, there are 30 independent ice hockey teams. Every of the teams will play 82 official NHL games every year. Many teams will have to travel from t

Interpretation of r – problems in interpreting r values, Interpretation of ... Interpretation of r - Problems in interpreting r values A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that th

Do all our activities involve mathematics?, Do All Our Activities Involve M... Do All Our Activities Involve Mathematics? :  The answer to this is 'yes' and 'no'. For those who look for mathematics and know where to look for it, it is 'yes'. For those who do

How many permutations can you make of the word statistics, Q. How many perm... Q. How many permutations can you make of the word STATISTICS? Solution:  There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'

Advanced abstract algebra, prove that J[i] is an euclidean ring prove that J[i] is an euclidean ring

Scientific notation, help me please .76 help me please .76

Trigonometry, sin30 sin30

Prove that the poset has a unique least element, Prove that the Poset has a... Prove that the Poset has a unique least element Prove that if (A, ) has a least element, then (A,≤)  has a unique least element. Ans: Let (A, ≤) be a poset. Suppose the po