Say we have a 2-variable function f(x,y) which is not defined at (x,y)=(0,0). I wanted to make this a continuous function in (0,0) by defining it to be of a certain value at this point. If the function was a single variable, I'd set it's value at x=0 equal to the limit of the function as x approaches 0. What is the equivalent method for above when it comes to 2 variables? Is it simply the limit as x,y approach 0,0? How would one calculate this limit, and if it didn't exist, would it be impossible to make f(x,y) continuous on (0,0)? An example of f(x,y): sin(x)/x2+y2

Q: Find all the points of discontinuity and classify them for the functions: x² + x (i) f(x) = x3 + x²…

A: Hey, Thanks for the question , "Since you have posted multiple questions as per our guidelines we…

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

A:

Q: Suppose f is a differentiable function such that f(-2) = 3 and f(5) = 17. Then there must be a point…

A: Consider the conditions for the mean value theorem.

Q: Show that the function f(z)= Im(z) is nowhere differentiable.

A:

Q: Reading a text message takes your eyes off the road for about 4.6 seconds according to a recent…

A: Conversion:- 1 mile = 5280 feet 1 hour= 3600 sec  Speed=DistanceTime

Q: The function f is given by f(x)=9.x^2/3+3x-6 has a relative minimum at x=? A. -8 B.-1 C.-1/8 D.0

A:

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

A:

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

A:

Q: find the critics (local max, lo cal min) Of the function f(xcy)= -x5+ Dy3+27x-24y+3

A:

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

A:

Q: Can you specify how you got the F=(y-x, x, y+x) on step 2?

A: The vector field F =(y-x, x , y+x) is given .

Q: Find the antiderivative F of f that satisfies the given condition F(1) = 2 and specify the domain of…

A:

Q: The function(x)= is concave down on which interval?

A: Given: f(x)=1x2+1

Q: Use the Cauchy-Riemann equation to determine if the function f(2) = x³ – i(2 – y)³ is analytic or…

A:

Q: Show that f(x)= |x| is not differentiable at x = 0.

A:

Q: I. Determine whether or not the function x2 + 2y if (x, y) # (0,0) f(x, y) 1 er-y if (x, y) = (0,0)…

A:

Q: F:(- 2, 2] → R, F(x) = [, (t- 3)(f² + 1) dt

A: Given, Fx = ∫-2x2t - 3t2 + 1 dtFx = ∫-2x2t3 - 3t2 + t - 3 dtFx = t44 - 3t33 + t22 - 3t-2x2Fx = x44 -…