Calculus of several variables , calculus homework help

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Obpun

Mathematics

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I am looking for the solution for 2.2 2.3 2.5 and 2.1

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10x 2 - 4x3 + OS The solution set of each of these equations is a 3-dimensional hyperplane in R4; the intersection of these two hyperplanes is the desired (2-dimensional) tangent and even Atiability, plane T. er of Exercises 22 nes, whic > condine a tanger rentiabi ine the heoren olumi .5.2 thog = 0 2.1 If F: RM → RM is differentiable at a, show that Fis continuous at a. Hint: Let F(a+h) - F(a) - DF (h) R(h) if h# 0. 1h Then F(a+h)= F(a) + dFa(h) + \h\R(h). 2.2 If p: R2 → R is defined by p(x, y)=xy, show that p is differentiable everywhere with dp(a, b) (x, y) = bx + ay. Hint: Let L(x, y)= bx + ay, a=(a, b), h= (h, k). Then show that p(a + h) -p(a) – L(h) = hk. But|hk|
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Explanation & Answer

here are two more question solutions.

Q2.3
Let us compute all of the directional derivatives at (x,y)=(0,0) . Let v  (a, b) .
We have,

ta  (tb) 2
0
f (o  tv )  f ( 0)
ab 2
(ta) 2  (tb) 2
Dv f  Limit t 0
Limit t 0
 Limit t 0 ...


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