lim X+x cos x 1- X → 0 sin x cos x 2 - lim(x + 3) x→2 |x + 2| x + 2 sin 5x lim X - 0 sin 4x 3- lim 4- h-0- 6- / 5h² + 11h +6 h

Q: sin? 0 sin 2x tan´ x 2. limøseco 3. lim 0→0 1 – cos 40 4. lim- x→0 sin 3x 5. lim -

A: Solution

Q: lim x approaches 0 ................ (1 + x + sin x) / (3 cos x)

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Q: •sin ² (x/2) = = (tan x sin x)/ 2tan x = sin ² (x/2) •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin…

A: 3) sin2x2=sinx tanx22=sin2x2 4) sin2x=2cos2(x/2)1-cosx=sin2x 5) 2sinx-sin2x/(2sinx+sin2x)=tan2x/2

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

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Q: limx0 cos x COS X 0-X. limr-o tan x limx-0 cot x

A: Definition and methods help to find the required limit of the given function. A value is said to be…

Q: sin(x)=−0.2cos(y)=0.4tan(z)=5.5 sin(−x)= 0.2cos(−y)= 0.4tan(−z)= -5.5 What does…

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Q: sinh (x) esin h-' (x) sin h- (x) Vx²+1 -esin h¯' (x) sin h Vx²–1

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Q: lim f(x) = -∞ x-2- lim, f(x) = 0 x--2+ lim f(x) =-3+ %3D X00 f(-7) = 3 f'(-4) = 0 f(-6) = 0 f'(-1) =…

A: The expression limx→-2-f(x)=-∞, limx→-2+f(x)=∞ shows that x=-2 is a horizontal asymptote. The…

Q: lim cot(z) %3D - 10 -1 0 3 0

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Q: Find the limits in Exercises 49–52.

A: we have given the limit function;

Q: Use the table to find the indicated limit.

A: Given tabular data is

Q: find the one-sided limit

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

Q: sin(x-3) 1. lim x→3 x²-4x+3 sin2x 2. lim x→n sin3x cos4x-cos2x 3. lim x→0_arcsin²3x

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Q: lim cos x x-0 , which among the following should result, in equivalent form, before L'Hopital's Rule…

A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

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: Exercise

A: Apologies. We only answer one question at a time. We will answer the first question as the exact one…

Q: lim 2 sin(-2 x) 0.3) 4 sin (5 x)

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Q: Trigonometric limits Evaluate the following limits or statethat they do not exist.

A: Consider the provided expression, limx→0sinaxbx Find the limit of the above expression. Apply the…

Q: Find the limits in Exercises 23–38

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the limits

A: limx→06x2cotxcsc2x=limx→06x2cosxsinx1sin2x limx→06x2cotxcsc2x=lim x→0   6*cos*x1sinxx1sin2xx…

Q: sin x cos x – tan x cos² x dx cos x cos? x sin x dx cos3 x 16. = sec x dx + cos x Let u = cos x ; du…

A: It is given that    ∫cosx-tanxcos2x dx We have to evaluate it.

Q: sin 3x (a) lim x-0 x (b) lim sin² 5x x-0 x2 tan? x (c) lim x-0 x2 cos? x – 1 (d) lim cos27 x – 1 (e)…

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Q: sin 14x lim x-0 sin 7x 3x (7x – 2) lim x+0 \7x + 3.

A: limx→0sin14xsin7xAs we know that if limx→a-f(x)=limx→a+f(x)=Llimx→0sin(14x)sin(7x)=00This is…

Q: iii. lim (1-sin x) tan x x→ I COS cos((x - 1)) iv. lim I-0 r³3r

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Q: f-\(x) = sin='(x) а. 2'2 f-l(x) = cos-'(x) (-) b. 2' 2 f-|(x) = tan¬'(x) c. [0, n] f-(x) = cot"(x)…

A: This is a problem of fundamentals of trigonometric identities. Please find the solution below.

Q: () lim x→0 .2 x cos

A: We have to find the limit: limx→0x2cos1x After putting limit value, limx→0x2cos1x=0×cos10 Since 10…

Q: sin(2 – x) (d) lim +2 x2 - x - 2 2x sin r (e) lim 140 1 – cos 4.x sin x – sin 1 (f) lim x - 1

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Q: lim *+ x cos x X0 sin x cos x

A: Given:       To determine: The value of the limit.

Q: ´sin x-sin x cos x lim x2

A: This can be evaluated as follows:

Q: Find the limits in Exercises 49–52.

A: Given: limx→π2-tanx, limx→-π2+secx ,limθ→0-1+cosecθ given limits can be evaluate as below…

Q: Find the limit

A:

Q: sin(3x) 6)lim x→0 sin(4x)

A: We have to evaluate the value of limx → 0 {sin(3x)/sin(4x)}

Q: lim sin (2 – 2) cot² (x² – x – 2)

A: We have to find

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

A:

Q: Find the limit

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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 x x0 sin Vx sin (x2 + x) 26. lim 28. lim sin (Vx-3) 30. lim x - 9

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

Q: sin (x) + cos³(x) = 1 - sin(x) cos(x) sin(x) + cos(x) sin (x) + cos°(x) - (sin(x) + cos(x)) (…

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Q: sin (3t) (d) lim 1-0 sin (8t) sin (x-4) (е) lim x→4 х—4 cos (2z)-1 (f) lim-

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Q: sin(3) (x – 6) – 3sin(x – 6) lim x-6 (x – 6)2 + 2(x – 6) + 3 – 3e*-6

A: We have to find the limit.

Q: lim cos (x) - Cos (y) 3. cos cy} Sin (e) - sinly'. பி Sin(x)

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Q: Find the limits in Exercises 25–30.

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Q: sin (1 cos x) sin x -0" sin Vx sin (x2 + x) 25. lim 26. lim sin (sin x) 27. lim 28. lim sin (x - 4)…

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Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx…

A: On solving this we will get

Q: Limits with trigonometric functions Find the limits in Exercises 43–50.

A:

Q: evaluate the limit.

A: Given integral is When x=0 Therefore, by applying L'Hopitals' Rule, we have

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: lim(x,y)->(0,0) = (1+x2+y2-cos(x2+y2))/(x2+y2)

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Q: sin x 25) lim x→0 5x 3(1 – cos x) 26) lim sin x (1 – cos x) 27) lim 2x2

A:

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.