Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² + y²

Q: Evaluate the limit. lim I->0 V1+ 7x -1

A: Using limit,

Q: Find the limit. x²y + xy² lim (x,y) → (3,-2) x² - y²

A:

Q: Find the limit. lim .. (x,y) → (5,5) - x²y³ – x³y2 x² - y²

A:

Q: Find lim (x,y)-(0,0) y7x⁹8x97y8 + x105 xy7 +x8

A:

Q: 2x -5x +2 3. Calculate the limit lim .2 x-2x X→2 X -3x +4

A: Limit of the function f(x) as x approaches  to a means as x approaches to a from left side and right…

Q: Find the limit. lim (x,y) → (9, 9) 3 3,,2 (x²√³ - x³y²2) -

A: Apply L'hospital rule in limit

Q: Find the limit. lim (x, y) (9, 4) X + 3y – 4x - 12 y 4 %3D У -4 6. 0. O 12

A: A detailed solution is given below.

Q: Find the limit algebraically. lim (V25x2 +x – – 5x)

A: the given limit is: limx→∞25x2+x-5x we have to find the value of the limit.

Q: Find the limit, if it exists: 3x2 + 4y lim (xy)-(0,0) x2 + y²

A:

Q: Find the limit if it exists, or show that it does not exist. xy lim (x,y)→(0,0) x2 + y8

A: Breaking it down to two steps, first putting limit as x tending to 0, then y tending to 0 because…

Q: Change the order of integration in the integral Reverse the order of integration. SS f(x,y) dy dx…

A: Sol:- To change the order of integration , first plot the graph of  x = y2 x = y

Q: – 4x + 8 if x 2 Find lim f(x) , if it exists. I2 O-5 O DNE 05

A: Function given is -        f(x)=-4x+8if x≤2-5x+5if x>2 We need to find limx→2f(x) if ity exists.…