Which option equalsS x sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x tanx + In|cosx| + C x tan2x - In|cosx| + C O x tanx - In(cosx) + C O None of the above O O O O

Q: 2. Suppose, f'(x) =2 cosx+sec x, -7<x<: and it is known that f()= =4. Find the function f(x)

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Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

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Q: d Select one: æ(sin=! æ)* 3x + 2 sin- x 3x x(sin x) -1 + 2(sin-1 x)? 1-a2 x² (sin-1 æ) 3(sin1 x) +…

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Q: 7. The value of A. cosx - C O A O B О с O D dx √(1-x is B. sin '(x)+c C. cosx ' +2¢ D. cosx

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Q: Determine ƒ such that (1, sin 1) is on the graph of f and e2z + 5e² + sin æ ifx 0

A: When derivative function is given, to find the actual function integrate the given derivative of the…

Q: Q3) Use the addition formulas to derive the identity of (cos (x --): sin x ) %3D

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Q: What substitution should be used to solve the integral O sin u=3x/2 sec u =2x/3 sec u =3x/2 O tan u…

A: We have to solve the integral

Q: Find f(x) given that: f'(x) = 2 cos x -3 sin x and f (주) %3D %3D

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Q: 2. Extend the identity cos(ax)-cos?x-sin'x for xE PR to the identity cas (a2)- Cos s 2-sinz for & €…

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Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: f(a) tan(x) + sec(x) simplifies to where cos(x) f(x)

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Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

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Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: y=x-2cosx Differentiate the function. dydx=ddx(x-2cosx)=1+2sinx

Q: Evaluate: /x?cos(2x)dx 2x2sin(2x) + 2xcos(2x) – sin(2 x) А + C 4 2x2sin(2x) – 2xcos(2x) – sin(2x) +C…

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Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

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Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = cos 3x/2 , 0…

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Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: 15. Evaluate f e sin2x cos 2x dx A. 2ecos 2x + C C. 2e sin 2x В. + C 2ecos 2x D. 2esin 2x + C

A: You need to have the idea how to use substitution in integration.

Q: Find the first four nonzero terms in a 6y"-(cos x)y'-y = 0; y y(x) = +... (Type an expression that…

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Q: Evaluate the given function tan?ydy = sin3 xdx is equal to. 30 3(tany – y) А. Зх + cos³x = cosx cosx…

A: tan2ydy=sin3xdxIntegrate both sides and solve.

Q: The sin(5x + 2x) dx cos5xcos 2x is equal to 2 In(sec 5x) + 5In(sec2x) +C А. 10 In(sec 5x) +…

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Q: Evaluate cos (x (x2 – 2x + 1) (2x - 2) sin (x 2 - 2x +1) (2 – 2x) sin (x? – 2x + 1) O (2x 2) cos (x-…

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Q: III) Prove: 2) cos x x + sin æ sin y = sin 3y (3) COS (2) for all x and y such that x+y= 2

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Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?     3/8…

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Q: Evaluate: / sec (5x + 1).5dx Select one: O cor(5x+1) + c O tan(5x + 1) + c O cor(5x) + c O tan(5x) +…

A: Use the substitution method and simplify the given integration than integrate.

Q: O https docs.google.. 48 Evaluate D(3 sin x+4cos 4x). A. 3 cosx-4 sin 4x B. 3cosx-16 sin 4x C. -3…

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Q: What is the multiplicity of the zero p = f(x) = 2 – 2 cos x? of Select one: 1 2 3 4

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Q: Which of the following is true? cos (x), cos (x) cos1°(x) O Ssin*(x)cos°(x)dx =- + C 10 A 4 ®…

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Which of the following tables has been completed correctly using exact values? Cos x sec x 0°…

A: We are required to find the value of sec x and cos x for different values of x between 0 degree and…

Q: 25. fx sec²xdx is a. x tanx - In cos x b. x tan x + In cos x c. x tan x-sec²x + C d. x tanx+sec²x +…

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Q: Evaluate the given function tan?ydy = sin xdx is equal to.. 30 3 (tany - у) А. Зх- = cos³x + cosx…

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Q: TO For x such that 0 < x<, the expression 2. V1-cosx V1- sin'x COS"X is equivalent to: sin x COS X

A: I am solving this in step 2

Q: Is f(x)=cos^2(x)-sin^2(x) even, odd, both, or neither?

A: Given,           f(x)=cos2(x)-sin2(x)

Q: х Given that t= tan , show that: 1-1? 2t d) sin x = 1+t? e) cosx = 1+1? 2t f) tanx = 1-?

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Q: Which option equals Sx sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x…

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Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: The suitable substitution to evaluate | sin² 4(x + 2) dx is None O A. - cos8(r +2)] [1- cos4(r+ 2)]…

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Q: Q4: Prove that: cos?x – sin?x = 1- tan?x cos?x

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Q: (a). Find a common denominator for COSX |- COSX and 1- COS x COS x –COS X COSX = cosx-coseX COS X…

A: a To find a common denominator for 1cos x and cos x1-cos x.b To expand cos x+tan x2 and to simplify.

Q: Which of the following is equivalent to [sin(-x) + cos(-x)]? 1 - 2sinxcosx O 1 O 1+ 2sinxcosx O…

A: Use Trigonometric identities and simplify.

Q: Use the Intermediate Value Theorem to show that sin x x2 – x has a solution on the interval (1, 2).

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Q: 22. Rewrite the expression as an algebraic function of x and y: sin(co os'x - tany).

A: Given, sincos-1x-tan-1y

Q: What is x sec xdx ? A. xtan x- In cos x+ C C. xtan x- In |secx+C | B. xsecx-secx tan x+C D. xsec x+…

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Q: The simplest form of tan2x is secx-1 Select one: a. tan x b. cos x +1 C. sec x + 1

A: Given:     To determine: The simplest form

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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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.