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Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: 3x+sinx-3 tan x -) Given g(x) = ln- calculate g'(x). %3D 3x4-Vx

A: Given gx=lnx3+sinx-3tanx3x4-x We know that lnab=lna-lnb. Therefore, using this formula we can write…

Q: Q: Find fo 1- y = tan/2/2x + 7 (x² +x)(x² -x+1) 2- y = x*

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Q: ((sin? 3x +x² tan' x)dx x) dx 2

A: Value is zero

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: COs x 10. S V4-sin2 x

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Q: cos2x – sin2x cos2x For +C: What is F(x)? dx= 3 cosx - sinx

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Q: Cos^2(x/2)=tan(x)+sin(x)/2tan(x)

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Q: sec" xtan y 4. For the function fS(x)-tanx, show that f*+y)-J69"-tanx tan y 5. For the function…

A: We use basic formula here, sin(x+y) = sinx cosy + cosx siny And Tan(x+y) = Tanx+ Tany/(1-Tanx.Tany)

Q: cos2x – sin2x cos2x dx3D -C. What is F(x)? For cosx – sinx

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Q: e lim Secx-1 Sinx (-esux) 3}r® २5 ९६० 5x 2 lim ーD6 Sin5x of Sin4x. e lim メーD6 よ + tan 38

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Q: cos(x) sin (2x) lim x X sin(x) – 1

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Q: cos2r – sin2x cos2x F(x) +C• What is Fx)? For dx= 3 cosx - sinx

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Q: Solve f ) = (tanX + Cos x and t Cos X

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Q: Evaluate f (2 cos x-sin x)² sin x

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Q: cos x + sin² x + 1 dx cos² x (sin² x + 1)

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Q: sin x dx coos x 6.

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Q: cos2x- sin2x cos2x F(x)+C: What is Fx)? For dr = - 3 cosx - sinx

A: A detailed solution is given below

Q: cos x lim

A: the given limit is                   limx→∞cos(x)x as the limit applied directly cannot give the…

Q: cos x tan x a) lim x→0 2x (x2 b) lim sin(x-) 4 x- 4

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Q: 3x2 tan x If f(x) find sec x f'(x) = Find f'(3)=

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Q: 2 |-cos X lim b. X - Sin x

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Q: 3x2 tan x If f(x) find sec x f'(x) = %3D Find f'(3)=

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Q: sin(cos x) limx-n/2

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Q: 3x2 tan x If f(x) find sec x f' (x) = %3D Find f'(3)=

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Q: cos(x) lim 2

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Q: cos((x) – sin(x) – 1 х) — 1 - 5. lim x→0 2.x

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Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

Q: cos2x – sin2x cos2x For -F(x)+C. What is F(x)? cosx – sinx

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Q: Cos“ x Find f'(x) if f(x) eT + V3x

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Q: (i) * cos x + cos x tan²x dx sec?x (ii) |x – 2| dx (iii) | x²/x* + 1dx

A: Since you have posted a question with multiple sub-parts, as per the company guidelines we will…

Q: Compare the accuracies of the approximations sin x = x and sin x = 6x/(6 + x2) by comparing the…

A: Given: The approximations . The functions and

Q: 2tan(x) dx 1 – tan2(x)

A: Solution:Given     ∫2 tan x1-tan2 xdxFormula:tan x =sin x cos xcos 2x=cos2 x - sin2 xsin 2x =2 sin x…

Q: cos(x) sin (2x) lim x sin(x) – 1

A: To evaluate the limit: limx→π2cos(x)sin(2x)sin(x)-1 Solution: limx→π2cos(x)sin(2x)sin(x)-1 On…

Q: Find the limit

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Q: x' cos“ x sin x dx. (л- Злх + 3х Evaluate: | -

A: For the solution of the problem follow the next steps.

Q: cos2x – sin2x cos2x For -dr =-F(x) +C. What is F(x)? dr%3D 3 cosx - sinx

A: We have to find F(x)

Q: lim 1-cosx/sinx ? x-->0

A: Given:

Q: cos2x – sin2x cos2x -F(x)+C• What is F(x)? For dx = - 3 cosx – sinx (sinx – cosx) - (cscx – secx) 3…

A: Please see the below picture for detailed solution.

Q: •π * (sin³ x)√1 + cos x dx 2

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Q: ) f(x) = 4 sin²(3x) - sin(3x) + 5.

A: As per the question we are given the following function : f(x) = 4sin2(3x) - sin(3x) + 5, And we…

Q: cos2x - sin2x cos2x / cosx - sinx) dx=1/3 F(x) + C. What is F(x)

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Q: cos2x – sin2x cos2x - -F(x)+C. What is F(X}? For dr =- 3 cosx – sinx -

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Q: sinx Q1//A- f(x) = COSX Required: lim f(x)

A: Given function is piecewise function so we have to evaluate the left hand limit and writer limited…

Q: sin(2x²)+x³ . Let f(x) = 0, df if x + 0 Then find- if x = 0 dx x=0

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Q: cos2x – sin2x cos2x F(x) +C. What is F(M)? For dx%3D cosx – sinx 3

A: A detailed solution is given below

Q: (c) Graph f(x) = sinx, 0≤x≤ 2π and also graph f-¹(x).

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Q: cos2r- sin2x cos21 =-F(x)+C What is Fx)? =xp For COSX – sinư A 2. --cos 'x- cosT+-sin't 3 cos'x sinx…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: cos2x – sin2x cos2x For -dx=÷F(x)+C. What is F(x)? cosx – sinx 3 A (sinx – cosx) ® (cscr – secx) 3 2…

A: topic - indefinite integral

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.