QI Evaluate the following [Choose six only). (1): 2 if y = 5 cos 2u and u=x +n. dx sin(y-4) i (2): lim,-16 x-16 (3): for t-g? 1.

Q: lim [(cos(rt) + 3) i +²j+ (3° +3) k] = t→0 lim [e'i+ 3r° j+ e'k] = t→1 lim [sin(3rt) i + 3f| = t→-2

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Q: ELIMINATION OF ARBITRARY CONSTANTS

A: The given solution curve is y=C1excosx+C2exsinx=ex C1cosx+C2sinx. That means, the roots of auxiliary…

Q: Z-T 4. Find all singularities in C for the function f (z) = and their residues. sin? 7

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Q: 1-sin t lim 1+cos 2t t- 2

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Q: Derivatives: using (4 step rule). 1. q(t)=10 + 5t – 1? 2. s(x)= 3-x ,2 4. f(x)=sin3xcos 3x 5.…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1-cos2 (x+y) 3. lim (xy)-(0,0) (r+y>)ety

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Q: x²+1 lim tan (x,y) → (0,1) x? +(y-1)². O is equal to 0. O is equal to -II

A: Given that: lim(x, y)→(0, 1)tan-1x2+1x2+(y-1)2

Q: 12. Find the first derivative of y = 2cos(2 + x?). A. -4x sin (2 + x²) B. 4x cos (2 + x*) C. x sin…

A: Since you have posted multiple questions. As par guidelines we"ll solve first question only. If you…

Q: COS X d) f(x)=3sin √√x³ -3x+2___ _e) ƒ(x)=! f) h(w) = 3 cos(tan w)

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Q: lim (x)-(.0) tan , -= (A) Does not exist (B) e? (C) 0 (D) ezn (E) e *IN

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Q: Find the limits

A: Our Aim is to find the limits of the following expression given below:-limx→0 sin (x) cot (2x) -(i)

Q: Find the limits

A: Given: Function  To Find: Limit of the function at the given point

Q: ). y² = 4x, 2x - y = 12 ). y = In x³, y = In x, x = e ):y = 2sin x, y = sin x from x = – to x : %3D…

A: As per bartleby guidelines for more than one part only first part is to be answered , please upload…

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: lim cos 3+5x – 2r2 85 – 2r2 – 19 lim ² +7 1 – cos 2r lim

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Q: sin 3y cot 5y Q7// Evaluate limy-0 y cot 4y

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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: cos(x) – sin(x) cos(2x) (c) lim (d) lim (cos())³/m²

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Q: Cos (x-y) t cos (Xty). COS 2cos x COSY

A: (Cos(x-y) + cos(x+y)) /2.cosx.cosy =?  We know that cos(x-y) = cosx.cosy+sinx.siny…

Q: (arctan o tan)' = 1 – pi k E z°(k +1/2)pi When differentiating on the Real line is this true?

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Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: lim h→0 (e) cos( 4 + h) h 1

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Q: e-3sin z (c) lim x² (d) lim sin(rx) lIn (x – 1) x→1+

A: The given limit is: (c) limx→∞e-3sinxx2  To find the value of the limit.

Q: O Lim tanx メーンク メ と5 5+s2 2Lim S+1 ン4 3) Lim 3-→ yリアンチアン49 6+ )Lim I+ Cos メ→

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Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: lim cos x + x cos a. 0 b. 1 d. does not exist

A: This question is based on Squeeze theorem.

Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: cos(x) lim 2

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Q: cosh (T- i) = %3D e cosl i e sin 1 + e- cos 1 + i e- sin 1 e cosl i e sin 1 + e-TI cos 1 ie- sin 1 2…

A: We know formula of coshx in term of exponential form

Q: cos cos 30 - cos 50 lim- 0>0 s 70 - cos 90 cos

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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: f(z) = -6.6 sin (0.5z) + 4.2 cos (0.5z) Maximum value of f(x) occurs at z = What is the value of…

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Q: sin 3y cot 5y Evaluate limy-0 y cot 4y

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Q: Cycloid arch: x = a(0 – sin 0), y = a(1 cos 0) - -

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Q: Find the limits

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

Q: Q3/ lim Evaluate 2 (1+ cosx) ) sec x

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Q: sin(2h)(1 – cos h) h2 lim

A: Consider Then simplify the function

Q: 2-t+ sint 45. lim t+ cos t

A: We have to find he limit: limt→-∞2-t+sin tt+cos t

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: x² – 9 2. lim x →- 3- x+3 (4 + h)² – 16 4. lim h-0 h sin2x 6. lim t tan³x

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Q: 1. Using Half Angle Substitution cos x dx Find= S 2-cos x

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Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: e Lim 2. 5+s2 y4 3 Lim (4) Lipn J+ Cos늦

A: 1. lims→∞(ss+1)(s25+s2)lims→∞s×s2s×s211+1s11+5s2= 12×2=14

Q: Find the limits in Exercises 9–12

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Q: 1+ cos x (b) lim x→T 1 – COs x

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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

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.