9. Evaluate the limit Y – 2 lim (x,y)→(4,2) Vx² – 4 10. Evaluate the limit cos(x) sin(y) lim (x,y)→(0,0) 11. Evaluate the limit xy lim (x,y)→(0,0) x² +y² ° 12. Evaluate the limit 2² – y? lim (x,y)→(0,0) Vx2 + y²

Q: (a) f : R² → R, f (x, y) = V1+x²y²-1 x2+y² (0,0) (b) ƒ : R² → R, f (x, y) = sin(x*y²) (x²+y²)² » (2²…

A: (a) Given fx,y=1+x2y2-1x2+y2,  0,0. Investigate the limit of fx,y at the point 0,0.

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

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 5. Use polar coordinates to find each limit : x³ + y³ lim (x,y) →(0,0) x² + y² (a) (b) lim (x,y) →…

A:

Q: Let f(x, y) = and let 8x2 + 9y2 L = lim(#,y) >(0,0) f(x, y). Which of the following statements is…

A: Option A is correct

Q: 6. Let r(t) = <-X²₂00- (a) Find lim r(t). k→0 (b) Find all values t and k for which r(t) is not…

A:

Q: 1 I. x² +y³).sin- x³ +y³ lim (х, у) -(0,0)

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: 1. Find the limit, if it exists, or show that the limit does not exist. (a) lim xy cos(x - 2y) (x,y)…

A: This question is related to limit of several variables function

Q: (iii) Find the directional derivative of f at the given point in the direction of v. f(x, y, z) =…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: For a certain function f(x, y). lim-0 f(t, 0) = 0 and lim 0 f(t, 3t) = 0. Does this mean that the…

A: Given- For a certain function fx,y it is given that limt→0ft,0=0 and limt→0ft,3t=0  To Check- If the…

Q: lim f(x, y) = L and f is defined at (a, b), then f(a, b) = L. If %3D (z,3)→(a,b) O True O False

A: Let us define a function:f(x,y)=3x+4y , (x,y)≠05, (x,y)=(0,0)This shows that…

Q: lim (x, y)→(0, 0) sin (x² + y²) x² + y²

A:

Q: lim (x,y) → (1,0) lim ~x, y) + (0,0) lim (x, y) + (0,0) tan - (x ² - 4 xy + y²) Scanned with…

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Q: 8. Čalculate the following limits. 22 – y? lim y + 4 (a) (x + y) (b) lim (x,y)-(2,-4) x²y – xy + 4x2…

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Q: Find the limits. Enter "DNE" if the limit does not exist. lim (1,y)→(7,6) Vy DNE 1 lim (z,y)→(9,4)…

A: we have to find the following limits

Q: 2x - y- x* lim (x.y)→(0,0) x² +y´ Find the limit, or show that the limit DNE. a) b), lim (x.y)>(0,0)…

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Q: 6. Determine the limits obtained by approaching (0,0) along both the x and y What does this say…

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Q: 2. The value of lim is (z.v)-(0,0) Vr² + y? (b) 1 a) 0 (c) 2 (d) does not exist

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Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: 1. Let f(x, y) = 2 – Vy +3° (a) Identify and sketch the domain of f. (b) Find equations of the level…

A: Given fx,y=x2-y+3

Q: 3. Given the function: f(x, y) = for if (x, y) + (0, 0). x* + y" (a) Find lim f(x, y) along the…

A: