f(x, y) = ´x cos(y) + y(e² − 1) xy 0 x=0 x = 0.

Q: Which of the following functions are continuous on (-0, 0)? (a) ƒ(æ) = 1/x. (b) g(x) = Va. (c) h(x)…

A: Topic = Functions  Correct letter is C

Q: ecos-1 x if x 1

A: If a function has to be continuous  then it must to follow below Left hand limit = Right  hand limit…

Q: { 2xy? 9x2 + y4 (x, y) # (0,0) (x, y) = (0,0) f (x, y) ·

A: Topic = Limits and  Continuity

Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ"(x)(x − b)dx - a

A:

Q: Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)?…

A: Given that f is continuous at 4,6 and that f4,y=y3 for y≠6. We have to find the value f4,6. Since,…

Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

Q: Use the definition of the derivative f'C)=lim flxty-PG4. to compuke derivative of flx)= 3X-X

A:

Q: x +1 x 2

A:

Q: 1. (y-1) x²+4 Cy-1)² (x,y)# (0,1) f(ox,y)= %3D (x,y) = (0,1)

A: Explained below...

Q: Make sure you do your best to answer all three parts. Suppose f(x) and F(x) are continuous functions…

A:

Q: sin(xª + y²) x² + y² 10.3.11. f(x, y) =

A: For function to continue at the particular point it's right hand side limit and left hand side limit…

Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Suppose f is differentiable on an interval containing a, b, and let P(a,f(a)) and Q(b,f(b)) be…

A: Given information:Suppose f is differentiable on an interval containing a, b, and let P(a,f(a)) and…

Q: { 2xy? 9x2 + y4 (x, y) # (0,0) f (x, y) = (x, y) = (0,0)

A: We will discuss limit by using different paths.

Q: tan-1(x) sin x f(x) = 1 for x 0, for x = 0, x²ln(-x)+x+1 for x < 0.

A: f(x) is a descrete functionWe have to find f(x) is continuous and differentiable at x= 0 or not

Q: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

Q: 2x3 + xy? x² + 2y4 if (x, y) # (0,0) if (x, y) = (0,0).

A: See the details solution in below