Question: 2. Let 3 4 2 x my , f(x y) = x24y2 1f (flag) 75 (0,0) 0 if (ray) 2 (0,0) (a) (6 marks) Is

2. Let 3 4 2 x my , f(x y) = x24y2 1f (flag) 75 (0,0) 0 if (ray) 2 (0,0) (a) (6 marks) Is f differentiable at (0, 0)? Prove your answer. (b) (6 marks) Find the directional derivative Du f (0, 0) for a general unit vector u = u1i+ U2 j. If it does not exist, explain why

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!

1. 6 If f(z) = (5;1:2 + 6) , find the following. You do not need to simplify your answers. fla) = \\ \fGiven that f(z) = zh(z) h(-1) =2 h(-1)=5 Calculate f'(1). ' Hint: Use the product rule and the...

Curve Sketching - Polynomials We're going to do the Curve Sketching Algorithm. f(x) = x5- 5x3+ 4x f' (x ) = 5x - 15x7 + 4 f" (x) = 20x - 30x A: Domain: B: Intercepts: y-int (0,0) x-int (op) (-1, 0),...

Is the function defined by 2x 3 if x 2 2x 3 if x 2 6 f x x 8 f x x 0 continuous at x 0 At x 1 At x 2 Find all points of discontinuity off where fis defined 10 f x if x 0 if x 0 NO x 1 if x 1 x 1 if x...

2. Let f (x) = sin x. a. Plot y = f (x) on the interval [0, 7 ] in the space provided. Include the rectangles produced using Right-Hand Riemann Sums with n =3 to approximate the area under f on the...

I am required to write c++ program to construct the natural cubic for f (x) =1/(x^2 + 1) using the data points at x = -8,-6, -4, -2, 0, 2, 4,6, 8. I am required to implement the systematic procedure...

A A Wrap Text General Paste BIU- a-A Merge & Center - $ % 4.000 2000 Clipboard Font Conditional Format as Cell Formatting Table Styles Styles Alignment Number U4 > K 3 B D E H M 1 This Excel exercise...

Using the graph and table as a reference identify the Domain of the function f x Write your answer in Interval Notation 5 4 3 10 1 2 3 4 f x 1 4 f x 0 11111111111111 0 14285714285714 0 16666666666667...

A A Wrap Text General Paste BIU - a-A- Merge & Center - $ . % +0.00 600 7.0 Clipboard Font Conditional Format as Cell Formatting Table Styles Styles Alignment Number U4 K P 3 5 B D E H M N 1 This...

if possible post as many pics so i can read it. thank you! A A Wrap Text General Paste BIU- o-A Merge & Center $ . % +0 2000 Clipboard Font Conditional Format as Cell Formatting Table Styles Styles...

ASSIGNMENT PROBLEM For the assignment problem, refer to Chapter 2 of the textbook (pages 41 - 42) The following table shows the truth table for the 7-segment display driver, and the figure shows the...

Assume the intensity of sunlight is 1.00 kW/m2 at a particular location. A highly reflecting concave mirror is to be pointed toward the Sun to produce a power of at least 350 W at the image. (a) Find...

During March, the production department of a process operations system completed and transferred to finished goods 20,000 units that were in process at the beginning of March and 110,000 that were...

Assume that Amazon.com sells the MacBook Pro, a computer produced by Apple, for a retail price of $ 1 , 5 3 0 . Amazon arranges its operations such that customers receive products directly from Apple...

In Ecuador, cut roses are one of the countrys leading exports. Prior to advancements in the air transportation industry, this would have been impossible as roses must be sold within three to five...

7. One or other combination of 16.

1. Discuss the following statements: a) Mastery is not the same as understanding. b) Being bigger than is not the same as being the thing that is bigger. c) The difference between order and disorder...

5. It is the needs of the individual that are important.