36. lim tan cos (sin x!/3) 37. lim cos 38. lim Vcsc² x + 5V3 tan x V19 3 sec 21 (Fn) 40. lim cos (In V) 39. lim sin

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

A: This is a problem of Differential Calculus.

Q: Number 33

A: Given,

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: For (cos(2x) – sin cos(x) – sin(x) - sin(2x) cos (2x)) +C. What is F (x)? A sin cos³ (x) – cos(x)…

A:

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

A:

Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

A:

Q: 1. sin (5x + ) sin ( x + T /2) %3D 2. tan (3x – T/2 ) = cot 2x 3. COs (x + п /2) sin ( T /2 – 2x )…

A: Given that three trigonometry equation  To find fundamental solution of the question

Q: verify the results  sin 4x = 8 cos3 x sin x − 4 cos x sin x  tan2 x =1−cos 2x/1+cos 2x

A: To prove: sin 4x = 8 cos3 x sin x − 4 cos x sin x Proof: Since sin2x = 2sinxcosx sin2(2x) =…

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: find dydx 15. y = (sec x + tan x)(sec x - tan x)16. y = x^2 cos x - 2x sin x - 2 cos x17. ƒ(x) = x^3…

A: To Determine: find the derivative  Given: we have y=secx+tanxsecx-tanx Explanation: we have…

Q: 1+3x- cOs x 2.) lim tan x

A: In this question we need to find limit of the given function.

Q: sin- In2 4+ tan-'cos- dx 2 2 I+ cos2* 4+ tan-'cos- In2 4+ tan-'cos- dx 2 2sin- 2 A 1+ cos 4+ tan…

A: To evaluate: ∫sin x2 ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: lim sin(k/n). 1. cos(1) +5/3. 2. cos(1) +1/3. 3. cos(1) +2/3 4. cos(1) – 1/3.

A:

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

A:

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: 7 it y= sina 4x- sin" 4x, #ind y' 2 8. it y= cos Gx +sina 8x, #ind y' キind a. Find the Intervals on…

A:

Q: Find the value of* cos(x) sin (2x) lim sin(x) – 1 - O 0/0 4. O (intinity)

A:

Q: 3. Show that Σ L 1 L-x= 2 2nnx sin L 0<x<L.

A: Let f(x)='12L-x Fourier half range sine series in 0&lt;x&lt;L is bn=2L∫0Lf(x)sinnπxLdx…

Q: y=2sinh(In x) Find: (y')(x^2) 2. y=cot(sin x^3) Find: (y')(x^-2 sec x^3)

A: (1) Given yx=2sinhlnx We have to find the y'x2 Differentiate yx=2sinhlnx with respect to x…

Q: sin(-æ) = - %3D V2 tan(x) = – %3D cos(x) csc(x) cot(x)

A:

Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

A:

Q: 2. 2. COS X Sinx lim 4x-X

A:

Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x…

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Q: 8 sin x cos x sec x =

A:

Q: 1. f(x)= xsin x 2. f(x) = x?cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) =

A:

Q: 2cos(2x)sin(2x)-sin(2x)=0 Interval [0,2pie)

A: Given that the trigonometric equation, Solve the equation for x,

Q: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

A:

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 1. f(x) = xsin x 2. f(x) = x²cos 2 x 3. f(x) = tan x – sec x sin x

A:

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

A:

Q: S tanx 1+ COS X JX

A: Given problem:-  ∫tan(x)dx/(1+cos4(x))

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: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

Q: 4sin'x – 1 1. 2sinx + 1 = 2sinx – 1 sin'x – 2sinx + 1 2. = sinx – 1 sinx – 1 3. ( sinx - cos x)(sinx…

A: Simply use the basic concepts of algebra and simplify the each one.

Q: 5- Show that a) sinh (z + ni) = – sinh z c) tanh(z + i) = tanh z

A: The complex function is of the form z=x+iywhere x is the real part and y is the imaginary part. A…

Q: 2 sin (4x) lim 2. x2 (1+ cos x)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: tanx 4 – lim 0 Cos[1– –] X 0.7 O 1.5 O 0.5

A:

Q: Find f'(x), if f(x)= tan² 4.x. Find f'(x), if f(x) = sin² 2x./cos 2x . Find f"(x), if f (x)= Inx+…

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Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

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Q: 37. cos 6x dx 40. sin x? dx 39. cos do 42. tan x sec² x dx 41. sin 2x cos 2x dx csc2 x dx cot x sin…

A:

Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3D cOS x 1+2y + cos x-sin x 1+ sin x 1+ 1+ cosx 8.…

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Q: 2) tan-l 1 Vz 4) sin-! 6) tan-1V3 8) tan-l 0 V3 10) sin-! V3 12) tan- 2. 2. 3.

A:

Q: 1. lim sin x sin 2x x-0 1-cos x 3x+x+2 . lim X-4x3+8x+1

A: d) To evaluate                       limx→0 sin x sin 2x1- cos x                            =sin (0)…

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x…

A: Introduction :

Q: Solve over the interval [0,2pi)

A:

Q: sin- In2| 4+ tan¬'cos- dx 2 2 1+ cos- |4+ tan-'cos= 2 2sin- In2| 4+ tan-'cos- |dx 2 2 A 1+ cos2…

A:

Q: Find 2 sin(x + sin(x + sin a)) – 2 cos(cos 1) lim 2x – T ithout using L'Hôpital's Rule.

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.