Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0 arctan(@) + C 2 + O arctan 0 + arctan(0) 0 +C 2

Q: Integrate -- | cos 5xcos x a) 0.5 b) c) d) 2

A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: 2. (a) Use algebra to verify that (1+ (x – 1) (b) Differentiate arctan(x+1) – arctan(x- vital thing…

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Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Evaluate [[ sin(y²)dydx where 2: 0<y<1, 0<x<y°. 0 x b) a-cos¢x)) (1 a) 1-cos(x) 1 - cos(1) c) 2 d)…

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Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

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Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

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Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: nx and y=cosx from x=- to x=- 4 4

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Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

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Q: If f (x) = A (В B C D Stams. 0 sec²x tanx 1+1² Ite¹ 1+e tanx sec ³x 1+e -dt, then f'(x) equals tanx…

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Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

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Q: a) Differentiate f(x) = sin x from first principtes. %3D

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Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

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Q: Issol za 53. f(x) = VxIn x on (0, co) %3D

A: Given: 53.   fx=xlnx,  0,∞

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

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

Q: 2 = using the relation r= VT show that sin x %3D EX II

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

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Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

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Q: The f xcos x² 1-sin x2 dx is

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Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

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Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move…

A: Given force f(x)=x2-cos(3x)+2

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: Find all the singularities of tan(z) f(z) = determine their types, and compute the residues at the…

A: Given function is fz=tanzz. We have to find the singularity of fz. Now, limz→0fz=limz→0tanzz00…

Q: sec22ydy cotzy(3+tan?2y) : 1n(3 + tan?2y) + C D. - In(3 + tan²2y) + C Evaluate the integral: J 1 С.…

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Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: I* cos z lim 1³+2

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Q: Obtain the GENERAL SOLUTION tan'ydy = sin xdx xdx-Sa²-x² dy =0 y'exyz

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Q: Obtain the approximate answer for 2 cos(x )dx using the trapezoidal method so 3) that the maximum…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e…

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Q: Evaluate tan-1 x dx А. 1. tan-x dx = x tan-!x-;In(1+x²) + C В. 1. tan-x dx = x tan-x+;In(1+ x?) + C…

A: As we know that the expression for the integration by parts: ∫udv=u·v-∫v·du Given: I=∫tan-1xdx or…

Q: In (tan (x)) dx. 3. Evaluate J sin(x) cos(x)

A: NOTE: Refresh your page if you can't see any equations. . ..............(1) substitute  take…

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: dy - y tan x = 10 tan x dx ution of y(x) using two different techniques. Hint: tan x dx = - In(cos…

A: We have to solve given problem: First method:

Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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