Consider the function (a) Show that is continuous at the origin. (b) Show that x
Question:
Consider the function
(a) Show that ƒ is continuous at the origin.
(b) Show that ƒx and ƒy exist at the origin, but that the directional derivatives at the origin in all other directions do not exist.
(c) Use a computer algebra system to graph ƒ near the origin
to verify your answers in parts (a) and (b). Explain.
Transcribed Image Text:
f(x, y) = 3√xy.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (6 reviews)
a b c fx yxy is the ...View the full answer
Answered By
Hillary Waliaulah
As a tutor, I am that experienced with over 5 years. With this, I am capable of handling a variety of subjects.
5.00+
17+ Reviews
30+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
(a) Show that the function f (x, y) = 3 xy is continuous and the partial derivatives f x and f y exist at the origin but the directional derivatives in all other directions do not exist. (b) Graph f...
-
Use a computer algebra system to graph f and to find f and f. Use graphs of these derivatives to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and...
-
The solution in Problem 1 might look smooth, but it might not feel smooth because the piecewise defined function [consisting of L1(x) for x 100 doesnt have a continuous second derivative. So you...
-
Gabriele Enterprises has bonds on the market making annual payments, with seven years to maturity, a par value of $1,000, and selling for $974. At this price, the bonds yield 7.2 percent. What must...
-
Explain why the indirect method of preparing cash flows from operating activities is also known as the reconciliation method.
-
Do you think the effects of TAFTA on each product you selected will be consistent with what advocates or critics of TAFTA might have predicted? The United States and the EU have agreed to negotiate a...
-
Excess Gibbs free energy models are used to determine the value of the (a) Isothermal compressibility (c) Coefficient of volume expansion (b) Activity coefficient (d) Gibbs' free energy.
-
Carrie D'Lake, Reed A. Green, and Doug A. Divot share a passion for golf and decide to go into the golf club manufacturing business together. On January 2, 2015, D'Lake, Green, and Divot form the...
-
Quilters Newsletter Magazine gave instructions on making a quilt. The quilt required 4 yards of white-on-white print, 2 yards blue check, yard blue-and-white stripe, 2 yards blue scraps, yard yellow...
-
Find the least squares regression line for the points. Use the regression capabilities of a graphing utility to verify your results. Use the graphing utility to plot the points and graph the...
-
A corporation manufactures digital cameras at two locations. The cost of producing x, units at location 1 is C = 0.05x 2 1 + 15x + 5400 and the cost of pro- ducing x units at location 2 is C = 0.03x...
-
An article in the Wall Street Journal, discussing large high-tech firms such as Amazon, Microsoft, and Google, stated, Todays high-tech giants may not be monopolies in the most classic sense....
-
Wumpus world has a game form where there is an Agent who has a mission get treasure stored in one of the grids in the Wumpus World environment which is 4x4 in size. In the Wumpus world environment...
-
6.45 - You and your friend Peter are putting new shingles on a roof pitched at 23. You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.3 m...
-
Write a python simple program using a function that takes in a number of seconds and returns a string that can be used to display that value in minutes and seconds. Notice that this function DOES NOT...
-
An isolated conductor of arbitrary shape has a net charge of +9.00x106 C. Inside the conductor is a cavity within which is a point charge q +3.15x106 C. = What is the charge on the cavity wall?...
-
A consumer has a current income of $60, which can be spent only on goods X and Y. The price of good X is $3, and the price of good Y is $2. a) Graph the consumer's budget constraint, clearly labeling...
-
What are the primary international sales closing techniques?
-
1. As a general strategy, would you recommend that Carl take an aggressive approach to capacity expansion or more of a wait-and-see approach? 2. Should Carl go with the option for one facility that...
-
A tsunami is an ocean wave often caused by earthquakes on the ocean floor; these waves typically have long wavelengths, ranging between 150 to 1000 km. Imagine a tsunami traveling across the Pacific...
-
Determine whether the following statements are true and give an explanation or counterexample. a. b. c. Differentiating the velocity equation for an ocean wave results in the acceleration of the...
-
Use a calculator to evaluate each expression or state that the value does not exist. Report answers accurate to four decimal places. a. coth 4 b. tanh -1 2 c. csch -1 5 d. e. f. g. csch x. 2 1/2 ON...
-
Vinand Petroleum, Inc.: Initial Audit Engagement and Fraud Risk Case for a Specialized Industry Regardless of whether you are inclined to agree or disagree with Nick Fraudus' point of iew, do you...
-
Cash flow table Year Cash Flow 2014 $1,500,000 2015 $2,300,000 2016 $3,000,000 2017 $3,400,000 2018 $1,800,000 Calculate geometric total return Annualized rate of return Prepare a 10 year cash flow...
-
Sonya Fuentez, an IRS-enrolled agent, has been contacted by Carlito Alverez, who is interested in having her prepare his annual income tax return. Sonya is a little apprehensive about the engagement...
Study smarter with the SolutionInn App