8. Let f(x, y) be the function x3 + y3 xy? Show that the limit lim(9)→(0,0) f (x, y) does not exist by setting y = mx and f(x, y) : showing that the limit depends on m.

Q: By considering different paths of approach, show that the limit xY COS Y lim does not exist.…

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Q: x²– y? lim (x, y)→(0, 0) x² + y?

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Q: 2.a²y rª + y? Show the function f(x,y) : has no limit as (x, y) → (0,0)

A: We have to show that the function fx,y=2x2yx4+y2 has no limit as x,y→0,0.

Q: Let f (r, y) = 5z'y 7+2y0 %3D Evaluate lim)(0,0) f (x, y). Either find the limit or show that the…

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Q: Find the limit. Enter DNE if the limit does not exist. lim (2,v) → (0,0) æ² + 14y²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 4. Does f(x) = : (0, 00) → R have a right limit at x = 0? If yes, compute the limit. If not, explain…

A: We need to calculate when x->o+ from right side then f(x) exist or not.

Q: - x² if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x…

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Q: Find the limit. Enter DNE if the limit does not exist. 15zy lim (2,9) → (0,0) 22+ y?

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Q: Find the limit lim (a,y) (-45,9) xy cos(x + 5y) (Enter 'DNE' if the limit does not exist)

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Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: Find the limit. Enter DNE if the limit does not exist. lim (x,y) → (0,0) x² + 12y?

A: Given limit, lim(x,y)→(0,0)x2yx2+12y2

Q: Show that the limit x²ycos y lim (x.y)→(0,0) 2x4 +y² does not exist.

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Q: Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove…

A: Given :                     lim(x,y)→(0,0) xyx2+y2          We know that if the limit exist, all…

Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

Q: evaluate the limit  limit as x approaches infinity of x+cos(x)/ x+1

A: To find,

Q: We have the function if (x, y) # (0,0), xy x²+y² f (x, y) if (x, y) = (0,0), (а) Find lim…

A: We have to find the following given conditions according to the given condition

Q: (a) Show that the limit xłycos y lim (x.y)(0,0) 2x4 + y2 does not exist.

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Q: Show that the limit does not exist. (x + y)² lim (1,y)→(0,0) x² + y²

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Q: Show that the limit xycosy lim (x.y)(0,0) 2x +y² does not exist.

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Q: (4-x-x² if x ≤1 if x > 1 2x 5 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y= x.…

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Q: Use a table of values to estimate tne value of the limit of lim Vx + 4 – 2 f(x) f(x) 2.

A: Consider: limx→0x+4-2x   Let fx=x+4-2x Since we have to calculate limit at 0 of fx=x+4-2x.  Make the…

Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

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Q: 9. lim 15 1 + (i/n)6

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Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

A: Given:dydx=y3+y2-9y-913,-2 lies on the graphTo find limx→-∞y

Q: Find the limit (2x + y)² lim (x,y)→(0,0) 4x² + v² (Enter dne if the limit does not exist)

A: WE CAN FIND LIMIT . So , we can find limit along the line y=mx .i.e, we can choose path.If for every…

Q: (4- x - x² if x ≤ 2 2x-7 if x > 2 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 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…

A: Find the limit approaching the origin along x-axis i.e. y = 0.…

Q: By considering different paths of approach, show that the limit lim (1,y)→(0,0) rª + y² does not…

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Q: Find the limits. Enter "DNE" if the limit does not exist. lim cos (x.y)¬(0,0) x' – y' x² + y² 4x lim…

A: Find the limits : Given :            lim(x,y)→(0,0)cosx7-y7x2+y2               =  cos 0-00+0…

Q: Show that the limit of the function does not exist xy lim (xy)-(0,0) x2 + y?

A: We have to show that limit of the function does not exist.

Q: Evaluate the limit sin(a – Vy) lim (2,y)→(1,1) x - y

A: Here, we will use the following formulas,

Q: 2. Use the definition of the limit to prove that lim (r+2y – 1) = 1. (1,9)¬(0,1)

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Q: Show the limit lim (x,y)→(0,0) x4 + y² does not exist.

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Q: Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y = x.…

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Q: 1. a. Describe the level curves of the function f(x,y) = %3D x* + y b. Show that the limit lim (2,y)…

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Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

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Q: 11. Show that the limit lim (z.y)→(0,0) r² + y4 does not exists.

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Q: 1) Show that the limit doesn't exists : 3x2 Jy 2). lim (x,y)→(0,0) x2 +y²

A: We have considered different paths y = mx. If the limit is independent of m then the limit shall…

Q: Show that the limit lim (r.y)(0,0) In(1 – a²) + yª r² + y does not exist.

A: First replace y=mx and then find the limit if the limit is dependent on m then the limit doesn't…

Q: Show that the limit xłycosy lim (x.y)→(0,0) 2x4 +y² does not exist.

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Q: Find lim,0 sin (-:). 6 Enter I for o, -I for -o, and DNE if the limit does not exist.

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Q: Evaluate the limit below. 1 lim (x,y)→(0,0) 1-x2-y?

A: limx, y→0, 011-x2-y2

Q: 1. Show that the limit does not exist. xy? lim (x,y)→(0,0) x² + y4

A: This question is related to limit in two variables.

Q: Determine lim In/xy. (x,y)(e4)

A: lim(x,y)->(e2,4)lnxy

Q: Find the limit of f(1,y) = as (r, y) approaches (0,0), if it exists. If it does not exist, show why.…

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Q: Compute the limit analytically using the technique of your choice: lim d) x→0 sin(bx)

A: