#### Question Details

(solution) Hello, Can you help me solve those questions in detail. Thank you.

Hello,

Can you help me solve those questions in detail. Thank you.

1. Let W R ! R2, .t/ D 2.cos t; sin t/. - Sketch and describe the graph of . 2. Find an approximate value for [5]

[15] a ´ 3:99 .4:98/2 sin.4:03?/

by setting up a suitable function f .x; y; z/ and using an appropriate linear approximation of f .

3. Consider the function

f W R 2 ! R; f .x; y/ D 4x 2 C y 2 (a) Plot and describe a contour map of f . [10] (b) Plot and describe the graph of f . [5] (c) Plot and describe the intersection of the graph of f with the xz-plane. [5] (d) Give a function R 2 ! R whose graph is the tangent plane to the graph of f at the point .1; 2; 8/. [5] (e) Find the direction of maximal increase of f at .1; 2/. [2] (f) Find the directional derivative of f at .1; 2/ in the direction toward the point .5; 5/. [3] 4. Determine if any of the following functions is harmonic.

(a) f W R 3 ! R, f .x; y; z/ D x 2 C y 2 C z 2 . (b) uW R ! R, u.x; y/ D x

2 3 [5] 3xy . [5] 2 5. Find the local maximum and minimum values of

f W D ! R; [20] f .x; y/ D x 2 C y 2 C 1

;

x2y 2 where D consists of all points .x; y/ in R 2 such that x; y ¤ 0.

6. Find the absolute extrema of [20]

f .x; y/ D 5 C 4x 2x 2 3y 2 on the region D consisting of all points .x; y/ in R 2 with x 2 C y 2 16.

**Solution details:**

Answered

QUALITY

Approved

ANSWER RATING

This question was answered on: * Jan 30, 2021 *

* * Solution~0001016764.zip (25.37 KB)

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free solution (Deadline assured. Flexible pricing. TurnItIn Report provided)

##### Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .

#### About this Question

STATUSAnswered

QUALITYApproved

DATE ANSWEREDJan 30, 2021

EXPERTTutor

ANSWER RATING

#### GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

- As a reference for in-depth understanding of the subject.
- As a source of ideas / reasoning for your own research (if properly referenced)
- For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

#### NEW ASSIGNMENT HELP?

### Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions.
New orders are original solutions *and precise to your writing instruction requirements. Place a New Order using the button below.*

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.