do f() dr where f() = - sin o + sin o cos o = sin ø(y cos o- 1).

Q: Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual…

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Q: What is the indefinite integral (anti-derivative) { cos(x) dx? ○ sin(x) + C cos(x) + C - sin(x) + C…

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Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

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Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: Find f'a) for f(x)= =Sinx 1- Cos X %3D

A: We have to find the derivative of the given function.

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

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

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: Solve the DE sinx siny dx + cosx cosy dy - O by separation of variables. A sinx cosy - C sin y B cos…

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Q: sin x dx V2-cos² x

A: Given : ∫(sin x/√2 - cos2 x) dx     ....(1)   Let cos x = t   Differentiating both sides w.r.t. x -…

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: Differentiate. y = e cos x + Cos( ex)

A: Given- y=ecosx+cosex To find- The value of the derivative of the above function. Formula used-…

Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: integral of cos x sin^3 2 x dx

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Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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Q: Find antiderivative of f(x) = cosx

A: We have to find antiderivative (Integral) of  f(x) = cosx  i.e ∫ cosx dx

Q: Show that sin x dx=1-cos t (0<x<t<}r).

A:

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: What is the antiderivative of sin^2(x) + 2sin(x)?

A: Antiderivative of sin^2(x) + 2sin(x) is given by,  ∫[ sin2x + 2sinx ]dx =∫sin2x dx + ∫2sinx dx

Q: Let 3 sin x + 7 cos y = 3. dy %3D dx d²y dx?

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Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

A:

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

Q: 2T COs x dx

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Q: Find dy if sin x + 1 = cos y dx²

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Q: (폭), Let f (x) = x5 sin- Then %3D f'(x) =

A: Given that, fx=x5arcsinx27To find f'(x)

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Q: cos z dz ar gral f

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

A: