Question: see attached Let g : R' - R be defined as g(x, y) = In(ax2 + by- + 1) with a > b > 0.

see attached

Let g : R' - R be defined as g(x, y) = In(ax2 + by- + 1) with a > b > 0. (a) Find P2,(0,0) (x, y), the degree 2 Taylor polynomial of g at (0, 0). Show all your work. (b) Prove that there exits a constant M > 0, such that In(ax2 + by- + 1) M - 1 5 ax2 + by2 bVx 2+ 2 (c) Using part (b), evaluate lim c In(ax2 +by2+1) , with c * 0. (x, y)-(0,0) ax2 + by2

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

need help to solve. see attached Let g be the function defined by g(x) = -x2 + 8x. Find g(a + h), g(-a), s(va), a + g(=), and ->. g(a + h ) = 9 ( -2 ) = s ( VB ) a + g(a) = Let g be the function...

see attached Let f : R - R be defined as 7- 3 - 13 f (x, y) = x 2 + 1/2 ' if (x, y) # (0, 0) 0, if (x, y) = (0, 0) Prove that that fx exists for all (x, y) E R but fx is not continuous at (0, 0)

Let g : R R be defined by g(x) := x + 2x2 sin(1/x) for x 0 and g(0) := 0. Show that g(0) = 1, but in every neighborhood of 0 the derivative g(x) takes on both positive and negative values. Thus g...

answer thes questions please 2. The graph of a function f is shown below. Let g be the function defined as g() = | f(t)dt 0 5 (a) Find g (0). 9(3), 9(6) (b) On what interval is g decreasing?...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

see attached Let f : [R2 > R be defined as x2+y2' _ 3 f(X,y)={ y if(an')75(0,0) 0' if (x, y) = (0,0) 3) Determine all points where f (x, y) is continuous. b) Find fx(0, 0) and fy(0, 0)

see attached Let f : R2 - R be defined as vex f (x, y = y tex (a) Find the linear approximation at (0, 1) (b) Using the result in (a) find the approximation error at (-0.01,1.1)

Let g : R R be defined by g(x) := x2sin (1/x2) for x 0, and g(0) := 0. Show that g is differentiable for all x R. Also show that the derivative g is not bounded on the interval (-1, 1).

3. Let f: R" -> R be defined as f(x) := |x]|. Show that f is not differentiable at 0. Show that f is differentiable for all x * 0, and find a formula for Vf(x) for x * 0. Hint: If you are having...

Please answer questions a to e according to the following formula, and give detailed steps and explanations Recall that for a function f : RN - R, the gradient is simply the N x 1 vector formed by...

If this diver has a mass of 150 kg ( including his diver gear), and a total volume of 0.14 m 3 , How much force is provided by the bottom of the swimming pool on which he is sitting?

Which describes the "Network Effect?" A platform becomes more useful as its total computing power increases. A platform becomes more useful as it is linked to more applications. A platform can lose...

Required 1 Required 2 Required 3 Required 4 Required 5 Complete the merchandise purchases budget and the schedule of expected cash disbursements for merchandise purchases. \ begin { tabular } { | c |...

X=6 x=6 Assume that you are a production consultant. The factory uses a CPM approach to a production run described by the activity network as given below. D E Based on your evaluation however, the...

2. In this chapter, the reader should reflect on the following concepts:

1. To provide an understanding that a person in a communication situation conveys three things at the same time: their position, basic interests and values.

4. What is meant by the statement: We are extremely limited in our willingness to allow others to put their own case in a social situation?.