sin(x? + y?) lim xy 45. lim 46. (x,y)→(0,0) /x² +y° (x,y)→(0,0) x2 +y²

Q: 6x2 sin(y) lim (z,y) → (0,0) 6x2 + 9y2

A: Since it is indeterminant form.  Therefore we can consider y=mx  And therefore after applying limit…

Q: f(x) = { cos x, xpi  which lim does not exist

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Q: 1-V lim 1-VE sin r lim 0 +1

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Q: lim (x.y)-(0,0) cos( x² +y2 (x, y) # (0,0) f(x, y) = (x, y) = (0,0) %3D is continuous at (0, 0).

A:

Q: sin 2z cot 8z lim z cot 4z

A: To evaluate: The limit limz→0sin 2z·cot 8z z·cot 4z . Formula used: limz→0sin azaz=1 limz→0tan…

Q: X – sinx (i) lim x2 d (ii) ( e2x · cos x) dx (iii) J tan 2x dx d (iv) dx ( sech 2x) 1 (v) -) dx S(…

A:

Q: 5. lim tan x cos y = 1 (x,y)→(,0)

A: To show :  lim(x,y)→π4,0tan x cos y = 1

Q: y? lim y→0 In cos y

A: Given the function in y,      fy=y2lncosy Objective is to find the limit of function as y tends to 0…

Q: sin(x² + y) x2 + y? 9. lim (r.y) (0,0)

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Q: lim (x,y)→(0,0) (2² + y²) sin x² + y² , + y?.

A: Answer is 0 Explanation is given below..

Q: sin(2x) limy→ 0+ X

A: Given:     limx→0+sin2x2

Q: lim (x,y,z)→(-37,2,–1) (cos(xz) + In(xyz) – x/37) (2т — 2)у (z,4)→(1,0) (x – 1)² + y² xy? - lim lim…

A: Given lim(x,y,z)→(-3π,2,-1)cos(xz)+ln(xyz)-x3π lim(x,y)→(1,0)(2x-2)y(x-1)2+y2 lim(x,y)→(0,0)…

Q: lim (x,y)→(0,0) r sin² y + y sin² a x² + 3y²

A:

Q: Lim (sec y - 1)/(sec 2y - 1) a) as y -> 0 b) as y -> pi/2

A: (a) As y -> 0, Lim (sec y - 1)/(sec 2y - 1) = (sec 0 - 1)/(sec 0 - 1) = (1 - 1)/(1 - 1) = 0/0…

Q: Find the limit

A:

Q: x – y - lim (x,y)→(0,0) Vx – Vỹ |

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Q: (x.y) (0.0) 5. lim (x.y)(1,7) cos(ry) 1-x- cos y Cos V

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Q: Find the limit

A: We write the expression using sin and cos

Q: sin(6a°y³) =? lim a,y)→(0,0) xl12 + y4

A: If we put (0, 0) along the line y = m x3 , then,

Q: sin(x² +y²) (11) lim (x ,v )→(0,0) 2 x +y 2

A: For finding limit in the simplest way we can change the given question in polar coordinates

Q: sin 3y cot 5y lim y→0 y cot 4y у cot

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Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

A:

Q: salvepE tany= Sin(2 +y) +Sin(x-y) (ans. secy= C-2 Casx)

A:

Q: sin 5z-sin 3z 14. lim,» +0 sin z

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Q: (c) lim sin 3r sin 2r I sin 5z 8r-3 2r³ +z+1 (d) lim

A: Given that:                        (c) limx→0sin(3x).sin(2x)x.sin(5x)(d)limx→∞8x2-32x2+x+1

Q: Find the limit

A: We will find the limit by substitution

Q: х — у lim (x, y)→(0, 0) Vx - Jỹ

A:

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

A:

Q: 21. lim (x.y)-(0,0) x2+y2 22. sin( x* +y?) lim (xy)-(0,0)

A:

Q: Find the limits

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

Q: 26. y = sinh x, y= e, x = 0, x= 2 27. y = Vx, y =;x, x= 9 28. y =x, y = 2.x², x + y = 3, x>0 II

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Q: ysiny limy-»o (y+siny)²

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Q: i. y = sinh-1 (x), ii.y = cosh-1 (x),x > 1 iii.y = tanh-1 (x), |x| < 1 %3D

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Q: sin(xy} lim (x.y) (0.0) t² + y

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Q: Prove the limit statements

A: limx→0x2sin1x=0 Now since the range of sinx is -1, 1, therefore -1≤sin1x≤1⇒-x2≤x2sin1x≤x2 Now,…

Q: sin(2(a? + y?)) 2(x2 + y²) f(x, y) sint as (x, y) → (0,0). Assume that polynomials, exponentials,…

A: Use limit rule to calculate

Q: Find the limits in Exercises 25–30.

A: we have to find the limits in the given following questions But since we only do the three subparts…

Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

A: Definite integration limit as sum

Q: ху cos хy (а) lim (x,y)-(0,0) 3x + y* x+ y (b) lim (x.y)-(0,0)

A:

Q: Find the limits

A: Solution:- We have to find the limit of the f(x,y)  lim(x,y)→π2,0f(x,y)=lim(x,y)→π2,0cosy+1y-sinx

Q: 2х x2 +2x+1 A 2ln|x+1| + +C x+1 1 - + C x+1 В -arc cot X 1 +C x+1 C arctan x+ D 2ln|x+1| - (x+1)?

A:

Q: (a) The volume produced by revolving the area enclosed by the first arch of y = sin(x) and the…

A: Given :   Y= sin x Integral of the first curve is 0 to pi Rotate around y axis that is x=0 Use the…

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

A: Given: lim(x,y)→(0,0) x2+sin2(y)x2+y2

Q: f(x) = 4 sin(x) + 4 cos(x),    0 ≤ x ≤ 2? Find the local

A:

Q: sin 3x . [T] lim S.M; x→0 ; ±0.1, ±0.01, ±0.001, ± 0.0001 sin 3x sin 3x X -0.1 а. 0.1 е. -0.01 b.…

A: Evaluate the limit for x→±0.1limx→-0.1sin 3xx=Sin 3x-0.1-0.1                    =-Sin0.3-0.1…

Q: sin 0 d) lime tan 0 sin z-cos z + 1 e) lim, 0 3z

A:

Q: Limits with Three VariablesFind the limits in Exercises 25–30

A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Q: ex+y (²+x*)siny Зх - 2y П. lim III. lim (x,y)¬{0,0), lim 2 x* +y" (х.у) -0,0) 1+e*-у (x.y)-0,0)

A: We have to solve given problem: