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.
-
If a fan buys a sports mortgage to USC football games by paying $130,000 in 10 equal payments starting now , and then pays a fixed price of $290 per year for 50 years (starting 1 year from now) for...
-
Extend the analysis of the laminar-flow reactor for a power-law fluid. Perform some computations using the PDEPE solver, and show how the power-law index affects the conversion in the reactor.
-
Seashell Corporation has 25,000 shares outstanding of 8 percent, $10 par value, cumulative preferred stock. In 2009 and 2010, no dividends were declared on preferred stock. In 2011, Seashell had a...
-
Campbell's Toy Co . purchases toys from a local manufacturer. Scooters have been the Company's best selling toy. During the Company's first year of operations, the following scooter purchases were...
-
Find the least squares regression line for the points. Use the regression capabilities of a graphing utility to verify your results. Use the graphing utility to plot the points and graph the...
-
A corporation manufactures digital cameras at two locations. The cost of producing x, units at location 1 is C = 0.05x 2 1 + 15x + 5400 and the cost of pro- ducing x units at location 2 is C = 0.03x...
-
Use the Excel template Gantt Chart to develop a Gantt chart for the early start schedule for the wedding project in problem 36. Explain and trace the projects critical path(s).
-
A company has an account payable to a U . S . company, a supplier of inventory, in the amount of US$ 1 7 0 , 0 0 0 . The payable was incurred when the exchange rate was US$ 1 = Cdn$ 0 . 7 9 . At year...
-
How would I make this program run without the use of an array class /********************************************************************************************** *Description: CatchThief is a...
-
Consider a duopoly with firms A and B , which engage in price competition ( Bertrand ) . Both firms offer homogenous products. Total costs are given by CA ( q ) = 1 0 q for firm A and by CB ( q...
-
How to update multiple listviews with multiple columns that has the name, total amount of the items in the name, quantity and total amount in total in the last row of the total. 1:59 Item name Num $$...
-
A restaurant advertises a range of drinks using imported dairy-free coconut drink as part of its cuisine theme. The drinks are served unpackaged with a variety of mixers and garnishes. Due to a stock...
-
Determine the payment required to settle the invoice on the indicated payment date. Invoice Invoice Date goods Payment received amount (S) Credit terms date date 775.50 2/10, EOM Aug 4July 30 Sept 5
-
A fast-food restaurant averages 150 customers per hour. The average processing time per customer is 90 seconds. a. Determine how many cash registers the restaurant should have if it wishes to...
-
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...
-
Plato in Meno discusses an innate trouble, on the off chance that not a conundrum, of doing investigate that can be summarized in the accompanying manner, "Assuming you realize what you're looking...
-
Supply is the connection between the cost of a decent and the amount ready to move costing that much. It very well might be addressed as a table or diagram relating cost and amount provided. Makers,...
-
If 50% of the men 18-34 years old watch television on Mondays at 11 PM, and 30% of those viewers watch Monday Night Football, what is Monday Night Football's rating among men 18-34?
Study smarter with the SolutionInn App