y cot 4y Lim y-0 sin? y cot2 2y

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: lim cos? x sin? x = 8.

A:

Q: tan (xy) = ? lim (x,y)→(1,0) y+ xy (a) 0 (b) (c) 3 (d) (e) 1 -/4

A: In the given question we have find the limit of the function of two variable s.t…

Q: sin lim-0 h z cos () a. ㅠ COS b. 플Cos() c. T sin ) d. e. 1 f. None

A:

Q: sin' y 10. lim y→x 1+cosy

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 sin y lim (x,y)→(0,0) x + |y|

A: Use the definition of limit to prove that the limit is 0. lim(x,y)→(0,0)x sinyx+y

Q: VI – 1 а. lim r→1 Vx + 3 – 2 1 – sin x b. lim COS x 2 2

A: To evaluate the given limits without using L'Hospital rule.a limx→1 x3-1x+3-2b limx→π2 1-sin…

Q: sin(x+ y) =1. (i) lịm (x, yH0, 0) x+y (ii) lim (x, yH(0, 0) y

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Q: a) cot x – tan x sec x(csc x – 2sinx) %3D b) cor y(sec²y – 1) = 1

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

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Q: 2. Y' = csc - y cot x ans. y sin x = x + C %3D

A: We know that; The standard form of the linear differential equation of first order is: dydx+Py=Q ;…

Q: (B) lim sinh r cot I (C) COs z lim

A:

Q: In Exercises 45–46, use polar coordinates to analyze the givenlimits.

A: Solution:Given45. lim(x,y)→0xyx2+y2, 46.lim(x,y)→0sin(x2+y2)x2+y2Formula:x=r cos θ, y=r sin θcos2…

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: 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: ху cos y с) lim (x.y)-(0,0) 3x² +y² ху d) lim (х.у)-(0,0) х2 + y? х*sin'y (х.у)-(0,0) х2 + 2y? e)…

A: We have to find the limit if exists or so that the limit does not exist.

Q: 1-cos y 2. lim y→0 sin2 y

A:

Q: -6 -5 -4 /-3 -2

A: It is required to match the graph with their corresponding trigonometric functions. Use the graphing…

Q: Find the limit

A: We write the expression using sin and cos

Q: 4х — Зу y? sin? x - lim (x,y)→(0,0) 2x +3y (b) lim (1,4)→(0,0) x²(y² + 1)

A:

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

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Q: I. lim .sin (x,y)→(0,0)

A: As per bartleby guidelines only one question should be answered once, please send each question…

Q: 2. y' = y+ 3y cot x

A:

Q: y2+sin y Lim y-00 y?+cos y

A: Given,          limy→∞y2+sinyy2+cosy

Q: x². y² = x² + y? cot x y = (1+ cot x) y = In(sin 3x) y = x2. e*

A:

Q: y? sin? x (c) lim (2,y)→(0,0) x4 + yª xy cos y (d) lim (x,y)→(0,0) x² + y4

A:

Q: sin h lim h→0 5h

A:

Q: Va + sin x - Va – sin x lim Do not use L'Hospital's Rule X-0

A:

Q: lim etti + t → 0 sin(2t); i+e-2tk) 2t

A: We have to find the value of  given limit.

Q: ジ+y Cot x = Sin 2 X

A: Consider the given differential equation.

Q: lim (sin? (x) + sec(x))

A:

Q: QI Evaluate 2 2 | 2y? sin(xy) dydx 0 x

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Q: sin(xy} lim (x.y) (0.0) t² + y

A:

Q: Y'' + Y = Csc X Cot X, Y(π/2) = 0, Y' (π/2) = 0

A:

Q: tan r I – sin r (a) lim (b) lim (c) lim tan r – sec a 2

A:

Q: Lim 2 Sin v2 t - 3 Sin t t → 0* t

A: Note that:- limt→0+sin tt=limt→0sin tt=1

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: Lim Y cot 4y y→0 sin? y cot2 2y 1)

A: According to guidelines we should have been able to solve only one question at a time #1

Q: (a) 2ry? 23+3y3 (b) 4x2+sin?(y) x²+y² lim lim (r,y)→(0,0) (x,y)→(0,0) (c) lim [2 cos(r) – 3e*] (d)…

A:

Q: xarctan (x) lim x-0 x2 – sin? (x) O A) +infinity O B) -forever O C) 1 D) none

A: We know that arctangent is tan-1x I=   limx→0xarctan(x)x2-sin2(x)=…

Q: nd lim sinx -b x2 our answer: b. 2b does not exist ear answer

A:

Q: sin 3y cot 5y lim y0 y cot 4y

A: Given limit is,…

Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5" %3D

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Q: lim (x, y) (3/2, n) y sin(x – y)

A:

Q: 3. (x, y)→(3,4) „(+ + }) lim Vx? + y² – 1 4. lim (х, у) —-(2, -3) x² + y x + y + 1 5. sec x tan y 6.…

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

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.