d) Let the function: f(x, y) = 3, < 0, Find the following limits: (i), lim (z.y)-(3,-2) f(x, y) , (ii) lim (2.y)(-2,1) f(2, y) (i), lim (2,-y)→(0,0) f(z, y)

Q: Give an example of two differentiable functions f(x) and g(x) such that: lim, 00 f(x) = lim, 0 9(x)…

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Q: lim If (2,y)(0,0) f(x, y) = 0 then lim f(x, 0) = 0. T→0

A:

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: Let S = {(2,0) = R² : 2 = R}. If lim f(x, y) = 0 then (2.9)-(0,0) f(x, y) = 0. lim (z.g)-(0,0)(8…

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Q: x?y x² + y² Define the function f: R² → R by ƒ(x, y) = if (x, y) # (0,0) if (x, y) = (0,0) (a) Let e…

A:

Q: lim f(x, y) does not exist, where (1,4)→(0,0) Show that f(r,y) (x² + y1)³

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Q: For the function of (x,y) f(x,y) = |x| + |y| draw the level set f(x,y) = 1, f(x,y) = 2.

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Q: If lim f(x, y) = L along the x-axis, (x,y)→(0,0) lim f(x, y) = L along the (x,y)→(0,0) and if…

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Q: What is the limit of f(x, y) %3D as x2 + y? (x,y) approaches (0,0) along the curve y = x?

A: Explanation of the answer is as follows

Q: Show that xy4 lim (x,y) →(0,0) x² + y8 does not exist.

A: Given :                     lim(x,y)→(0,0) xy4x2+y8 We know that if the limit exists, all paths…

Q: lim g (y) where, g (y) = = y² +5 3-3y lim 9 (y) y² +5 ify < -2 -9 lim g(y) 3-3y if y≥-2 y-2 ify <-2…

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Q: 2x*y lim (x,y)→(0,0) x8 + 6y²

A:

Q: ering different paths of approach, show that the function has no limit as (x,y)-(0,0). f(x,y)=- Find…

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Q: lim g (y) where, g (y) = = Jy²+5 3-3y lim g(y) y² +5 if y -2 ify <-2 if y≥-2 g(y) --1 = -1.9 √y²+5…

A: We can draw the graph of the function and interpret the limit  of the function.

Q: (a)f(1), (6) lim→1 f(x), (c)f (2), (d) lim,→2, (e)f(3), (f) lim,→3 yA y = f(x) 4 3. -1 1 2 3 4

A:

Q: Consider the function of two variables defined by f(x, y) = x³y² x6 + y² (a) Compute the limit of…

A: The given function of two variables is f(x,y)=x3y2x6+y4. (a) To Find: The limit of the function as…

Q: F (x, y) = 2xy(x²-y²) x2+y2 1) Find lim f (x, y) when (x, y) (0,0)

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Q: If f is a function then lim f(x, y) = f(2,5). (x,y)→(2,5) %3D

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Q: lim f(x, y) = 6, then f(1.9, 2.9) = 6- %3D (x, y) + (2, 3) If f(4, 5) = 3 Vf(4, 5) = (-3, 2) then…

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Q: [f(x,y)] 4- lim (x,y)→(a,b) Lg(x,y)]

A: Please see the answer in step 2

Q: lim g (y) where, g (y) = Jy²+5 3-3y lim g (y) y² +5 ify < -2 -9 lim g (y) 3-3y if y2-2 ify <-2 if…

A: Given :limx→-2gy where gy=y2+5if y &lt;-23-3yif y≥-2

Q: lim (x,y)-(2,4) x² +x/F-2y x-Vy %3D ||

A: Solve the limit

Q: lim g(y) where, g (y) = [y²+5 13-3y lim g(y) y² +5 ify < -2 y+ 2 lim g(y) 3-3y if y≥-2 ify <-2 if…

A: First we have: gy=y2+5      if y&lt;-23-3y     if y≥-2 Now, limy→-2 gy=limy→-2y2+5=9          if…

Q: Determine the set of points at which the function is continuous. if (x, y) # (0, 0) 5x? + y? f(x, y)…

A: We know that given function is continuous in its domain so we need to check only at point where…

Q: Find the limits. F(x) = 2x? - 3x + 4, g(x) = Vx+ 2 (a) lim f(x) x-2 (b) 9(x) lim g(f(x)) = X-2

A: We have to find the limit

Q: The domain of the function f (x, y) = y-x2 is A) {(x, y)|x 2 y²,y # F2} B) {(x, y)\y > x², x # +2}…

A: For any function y=f(x) the value for f(x)≥0 for the function to exist. The given function is a two…

Q: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

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Q: Let f(x, y) = x2 + y ²" (a) Find the domain and range of f. =-}, 0, . (b) Draw a contour map of f…

A: given function fx,y=xx2+y2 (a) find the domain and range of the function domain -1,1:x|-1≤x≤1 range…

Q: For the function f(x,y) = (a) Find x³y 3x + y² lim f(x,y) along any straight line y = mx.…

A: Given function .

Q: (x-y)2 Show that lim does not exist. (x,y)→(0,0) x²+y2

A: We have to find the limit.

Q: Determine the limits xy-y-7x+7 lim (x,y)→(1,4) x-1 lim x² (x,y) (0.0) x² + y²

A: 1. (x,y)→(1,4)lim​x−1xy−y−7x+7​We will factor the numerator:• Group the terms: xy - y - 7x + 7 = y(x…

Q: #1 Let f: IR→IR and Suppose What can you say you say about the value (x,y) = (1,3) f(1,3)? that lim…

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: