(а) Evaluate the following limits and verify your answer. 3y² +5xy + 2x 3y +2xy (i) lim (х.у)-3,-2) 4(x² – y³) (ii) lim (x.y)(0,0)x - Vr - y +1-1 (iii) lim (x.y)(0,0) y (Hint: use Two-Path Test) (b) Find the partial derivative, where g(x, y)= sin² (2x+ y). (c) Given z= In (2x +3y) with x = 2s' (t-s) and y = e"-39). Find the value of z, by using the chain rule.

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: 4 Find the limit: lim t+0 t 4 et – 1, (Enter undefined if the limit does not exist.)

A:

Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 х2-х-2 1-Vx 2. limx→1 1-x 2х 3.…

A: Part 1,Given,           limx→-1x+1x2-x-2

Q: 1. Find the limit if it exists. V2 + t – /2 – t - lim t→0 3t

A:

Q: 8. Calculate the following limits. V-Vy+1 /2x-y - 2 (a) lim (x + y + 1) (b) lim (2x – y + 4)…

A: We have to find the limits.

Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim 10 4x…

A: 2(g) Given limit is : limx→∞6x2-7x+14x3-7 To find the value of the limit.

Q: 6

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Q: Evaluate the following limits. 4– 3y2 – y --2 6 - y - y? 3 – 7x2 + 14x - 8 1. lim (1+ Vw)(2 – w² +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Draw the phase portrait for i=2 -1. If z(0) = 1/2, what are the limits lim z(t)?

A:

Q: 1: Find the limit 6x°y5 lim (x,y)¬(0,0) x6 +y10

A: See the attachment

Q: 8. Calculate the following limits. 3 + 4x² + 2y? xy – 2x – y + 2 (a) lim 2x2 + y? (b) lim…

A: (a) Limit does not exist. (b) The limit is zero.

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(7/2)-(tan x)" (2) limy-o…

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Q: Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

A:

Q: (-1)"f" cost =1--+ 4! 2 (2n)! In(1+t) =t-+ 3 -.+(-1)*-"4 +... n Yukarıda verilen cost ve In(1+x)'in…

A:

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

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

Q: 2²+3ry I²+y² (x, y) # (0,0) (x, y) = (0,0) f(x, y): Evaluate the limit, or use a two-path test to…

A:

Q: パーy (x.y)-(0,0) x + y 2.) Prove that lim does not exist.

A:

Q: x- 2 x <4 Estimate lim Ax) where fx) = %3D x+2 x24 12 10 -8- 8. 6 2 Limit does not exist.

A: Check the value of function nearer to given point of limit if they are equal only then limit will…

Q: find the slope of a curve y = x2-2x-2 at the point P(3,1) by finding the limit of the secant slopes…

A: Given yx=x2-2x-2           P3,1

Q: 3y +5xy + 2x lim (1) (z3-2) 3y +2.xy 4(x*-y*) (i) lim (10 x -y +1-1 lim (1.)-0.0) (Hint: use…

A:

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

A:

Q: Calculate the limit x – y + 4vx – 4Vy Vx - Vy lim(x.y) → o(0,0) | Choose an option: a) -4 b) 0 c)…

A: Answer

Q: Q4)A) Find the following limits (for two only). x+1 1. limy--17-x-2 1-VE 2. limy-1 1-x 2x 3. lim--0…

A:

Q: Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or…

A: To show that the function f(x, y) = 8x^2 y subject to 3x-y = 9 does not have an absolute minimum or…

Q: 8. Calculate the following limits. (*# y + 1) /2r – y - 2 (a) lim (b) lim (2r - y + 4) (a.v)-(0,0) r…

A: given,

Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

A:

Q: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

A:

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

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: 2. Find the following limits algebraically. Then support your conclusion numerically. x² – 3x – 10…

A:

Q: Along the path a = e" find %3D lim (7,y) (1,0) y²-6ry 3r-y-3 O 2 O -2 O-3 O does not exist 0 3

A: we have to find the following limit

Q: . Apply the two path test to make sure the following limit exist or not at (0,0) xy f(x, y) x³ +…

A:

Q: (3+4y-y is th e of lim y+ oy +3y+4)

A:

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: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

A:

Q: 1. Evaluate the limit: xy - y lim (x, y) → (1, 2) x² - x+2xy - 2y

A:

Q: Find the limit: lim (z,y) → (3,3) 4x4 - 4y¹ x² - y²

A: The given limit is: limx,y→3,34x4-4y4x2-y2  To find the value of the limit.

Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

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

Q: Evaluate the following limits, 4- 3y2 – y y-2 6 - y - y? 3 - 7x2 + 14x -8 5. lim 12 -1 2. lim t=2 12…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

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

A: lim(x,y)-&gt;(e2,4)lnxy

Q: F(x) Let F(r) = | 3e" dt. Find lim if it exists. If the limit does not exist, explain why.

A:

Q: Find the limit: 1+y² In lim (x,y)→(1,0) l22+xy/

A: Topic:- limits

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

A:

Q: 4 14 Find the limit of function f (x,y)=, (x²+y*)° at the point (0,0) through the path 413 a. 0 b. 1…

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Q: If y(x) is a solution of y' = (y+1)(50 – y) with y(0) = 0, what is the limit of y(x) as x approaches…

A: Given: yx is a solution of y'=y+150-y. Also, y0=0. To find the limit of yx as x→+∞. As, y'=y+150-y.…

Q: What is lim ZH00 2+1 4z2 A -2 в c) D) 1 E) The limit does not exist. 1/4

A:

Q: 2x Sí“(2t-2)² dt (a) Find the limit (if exist): lim 1 2х-1

A: