Question
Asked Aug 8, 2019
37 views

Question 2 Pratice 

3
(2)
(a) Show that the following limit does not exist:
2y2
lim
(x,y)(0,0)2+y
(b) Calculate all the first and second partial derivatives of the function:
f (x, y) e+y
This study resource was
ared via COurseHero.co
help_outline

Image Transcriptionclose

3 (2) (a) Show that the following limit does not exist: 2y2 lim (x,y)(0,0)2+y (b) Calculate all the first and second partial derivatives of the function: f (x, y) e+y This study resource was ared via COurseHero.co

fullscreen
check_circle

Expert Answer

Step 1

Part A

help_outline

Image Transcriptionclose

We know the following inequality |x2+y2 Now taking limit x2 lim (axy)-(0.0) 2 lm x 0 lm 0 (xy)-(0,0) x0 Therefore, by the squeeze (x.y)(0.0) lim 0. y2 0 So, by analogous argument we obtain the result lim (x.y(0,0) x2-y lim (x.y)-(0,0)2+; 0 exist which is equal to 0. The limit of Therefore, the given statement in the question is not correct

fullscreen
Step 2

Part b

Given,

help_outline

Image Transcriptionclose

Given, f(x, y) e*2+y2 1st derivative af (xy) ae _ex+y2 x a(x2+y?) . ex2+y2 x (2x 0) ax дх дх 2xe2ty2 = af (xy) (e+y2) ay ex2+y2 x a(x2+y?) ay ex2+y? x (0 + 2y) ay = 2ye*2+y

fullscreen
Step 3

     2nd...

help_outline

Image Transcriptionclose

2f(xy)(2xe2+y) 2e*2+y2 x) 2x ax2 дх дх дх = 2x X (2xe*+y)2e*ty' x 1 4x2 e2+y 2e*+y = 2e**+y"(2x2 1) a2f(x.y) af (xy) a 2x x 2ye*2+y 2x дудх ay ay дх ay = 4xye*+y*

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Limits

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Hello, How is tan^-1 (tan (6pi/7)=-pi/7 possible? I don't know how it should be a negative or to use...

A: First consider:

question_answer

Q: How can I get the result? Which is the result?

A: The given function is,

question_answer

Q: Which of the following is the power series representation for g(x)? +8 OA. B. k 8 1 k 0 k 0 8k O C. ...

A: Note that the function g(x) is not provided (here option (c) can also be a power series). So, we are...

question_answer

Q: If given the differential equation y''-4y'+4y=et, is there a way to solve it for possible solutions?...

A: we are given a differential equation as  

question_answer

Q: Use Newton's method to approximate all intersection points of the following pair of curves. Round to...

A: Before we get into the solution of the question, let's understand a bit about Newton's method. If xn...

question_answer

Q: 8xy′+4(ln x)y)(4) +5x3 y′=−6x4 y−9xy″   What is the order of the differential equation shown above?

A: The given differential equation is,  8xy′ +4(lnx)y4 +5x3y′ = -6x4y - 9xy″.The order of the highest d...

question_answer

Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).

A: We first write the given function in the form of the definition of the derivative.  

question_answer

Q: 18. CCT 11 The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a...

A: The quantity (in pounds) of a gourmet ground coffee sold at the price of p dollars per pound is give...

question_answer

Q: The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have...

A: Here, we are given that for a real number 1< p < 2 , the graphs of y=px and y=x have exactly o...