Answered: x'y 26. Let f(x, y) = x* + y? %3D (a)…

x'y 26. Let f(x, y) = x* + y? %3D (a) Show that f(x, y) → 0 along every line through the origin. (b) Despite this, show that lim(x.y)→(0,0) f(x, y) does not exist.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Related questions

Q: Evaluate the integral. (Use C for the constant of integration.) (x^2-25)^1/2/x^3 dx

A: To find:- ∫ √(x2-25)/x3 dx

Q: Use implicit differentiation to find y' and then evaluate y' at (-2,1). x In y + 6y = 3x ] y'l(-2.1)...

A: This question is related to differetiation. solve in step 2

Q: Find all the values of x such that the given series would converge. 4" (x – 7)" Σ n + 7 n=1 Answer: ...

Q: an be sold at a price of Sp. For x-p"-7p+600, find the rate of change of p with respect t ...

Q: b) E(-1)"+1 Vñ Inn n-1

A: The given series is: ∑n=1∞nln n which is an alternating series with bn=(-1)n+1nln n, n≥1

Q: Evaluate the integral. Show all your work. dx (x² – 1)32

Q: c. Describe in words the meaning of the question "For what value of Tis f(T, 20) = -49?" Then answer...

A: Find your answer below

Q: az and əs az e the Chain Rule to find for z = x²y3, x = s cos t, y = s sin t. at

A: We have to find derivative by chain rule

Q: Evaluate and state limit laws used

Q: n(-7)" Use the ratio test to determine whether converges or diverges. n! n=7 (a) Find the ratio of s...

Q: Use implicit differentiation to find y' and then evaluate y' at (3,0). 9 ey =x? - y? y' = y' (3,0) =...

A: Let's find.

Q: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

Q: proj„b is always less than |5 1|

A: We will use the definition of projection vector and will use the Cauchy-Schwarz inequality.

Q: A time study showed that, on average, the productivity of a worker after t hours on the job can be m...

A: Given:- A time study showed that, on average, the productivity of a worker after t hours on the job ...

Q: 1. Find lim,→0 k e'

Q: I ... LL #3 The amount, A mg, of caffeine in the body t hours after drinking a cup of coffee can be ...

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

Q: me limit below represents a derivative f'(a) Find f(r) and a lim h-0 (5 + h)² – 25 h. 10

Q: 1 dr r/1+ x6 (use trigonometric substitution) 3.

Q: Test the series for convergence or divergence. 3.7.11 (4n – 1) · (5n – 1) * 4. 9. 14... n=1 Part 1: ...

Q: In Exercises 9-26, find fx, fy, fx, fyy, fry and fyx- 9. f(x, y) = x²y + 3x + 4y – 5 10. f(x, y) = y...

Q: The following statement is TRUE except A. Derivative is the same as slope. B. A function is continuo...

Q: f(x)

Q: Differentiate y = 21/2 4 - x (4 – x³)'"2 -

Q: 2. Let E be the piece of the cone z = Va² + y² lying between z = 0 and z = 1, oriented with the 'out...

Q: Using the ratio of successive terms, what can you conclude on the given sequence increasing decreasi...

Q: This question has several parts that must be completed sequentially. If you skip a part of the quest...

Q: sec" y dy- (f) tan y

A: Topic = Integration

Q: -dx x´ +2x+3

A: The given integral, ∫xx2+2x+3dx

Q: 75 ft A pole stands 75 feet tall, An angle 0 is formeđ when wires of various (engths of r feet are a...

Q: Find the slant asymptote with limits

A: Given function f(x)=(x-2)(x+2)(x+1)(x+3)(x+1)

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

Q: The temperature at a point (x,y,z)(x,y,z) is given by T(x,y,z)= 1200e^(−x^(2) − 2y^(2) - z^(2)) whe...

Q: Sy²e3»dy

Q: Evaluate: a In(x + y) e-y. dy dx

Q: Find the value of (f o g)' at the given value. f(u) = u° + 9, u= g(x) = Vx, x=1 (fo g)'(1) = (Type a...

Q: -11m. ii. cos-1(cos()) CO 6.

A: Given problem:- cos-1(cos(11π6))=?

Q: A silver dollar is dropped from the top of a building that is 1317 feet tall. Use the position funct...

Q: Evaluate the given integral, where CC is the circle with positive orientation: 2-32 dz Sc C: 12 + il...

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two decima...

Q: Write the function in the form y = f(u) and u = g(x). Then find as a function of x. dx y= e - 10x Wh...

A: Given that:y=e-10xTo find dydx

Q: Find the equation of the tangent line on the function f(x) = arctan (x²) at the point (1,).

A: We can find the equation of tangent line to the curve as below.

Q: 20 18 16 14 12 10 8 D 6. 4 0 1 3 4 6 7 8 9 10 11 12 Quantity Suppose that supply and demand at a mar...

Q: 11+11-12=

A: Given that: 11+11-12

Q: Find the differential of each f (a) y = 1 + 4s dy =

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: For each of the following pairs of functions f and g, determine if the level curves of the functions...

Q: dw for w = dt xez,x = t2,y = 1– t,z = 1+ 2t. e the Chain Rule to find

A: Given query is to find the derivative using chain rule.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant ) ...

Q: Express the following functions in terms of function f where y=f(x). Professor Lapan's Helpful Hint...

A: We can solve both the part as below as per the instructions of Professor Lapan's Helpful Hint:.

Question

100%

xy
26. Let f(x, y)
(a) Show that f(x, y) → 0 along every line through the
origin.
(b) Despite this, show that lim(xy)→(0,0) f(x, y) does not
exist.

Expert Solution

Step 1

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
Use the limit definition to calculate the derivative at z = a of the linear function k(z) = 5z + 16.
Let f(x) = 2x2 - 3x - 5. Show that the secant line through (2, f(2)) and (2 + h, f (2 + h)) has slope 2h + 5. Then use this formula to compute: (a) The slope of the secant line through (2, f(2)) and (3, f(3)) (b) The slope of the tangent line at x = 2 (by taking a limit)
A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.
Let f (x) = 2x2 − 3x − 5. Show that the secant line through (2, f (2)) and (2 + h, f (2 + h)) has slope 2h + 5. Then use this formula to compute the slope of:(a) The secant line through (2, f (2)) and (3, f (3))(b) The tangent line at x = 2 (by taking a limit)
15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10) billion dollars. Assuming that the trends shown in the above models continue indefinitely, calculate the limits lim t→+∞ I(t) and lim t→+∞ I(t)/E(t) algebraically. (If an answer does not exist, enter DNE.) lim t→+∞ I(t) = lim t→+∞ I(t) E(t) = Interpret your answers. In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country. Could the given models be extrapolated far into the future? Yes or No