f(x) f'(x) C where C is constant x" where n is constant e* where e is the number e a* where a is constant sin(x) cos(x) k· g(x) where k is a constant

Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

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: * (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) =…

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Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

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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: Prove: sinh(x – y) = sinh(x) cosh(y) – cosh(x) sinh(y)

A: The basic relations we need to know to solve this problem are, sinh(x) = ex- e-x2cosh(x) = ex+ e-x2

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: integral (x 2 + 2x ) cos x dx

A: The given integral is ∫x2+2xcosx dx. It is known that ∫udv=uv-∫vdu. Let u=x2+2x   and  dv=cosxdx.…

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

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Q: Differentiate. f(x) = 4 sin(x) − 7 cos(x)

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Q: f (x) = cos(x) f(x) = tan(sin(x)) g(x) = In(2x2 + 4x + 3)

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Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: Let f : R→ R be a differentiable function. Then for all x € R, the derivative of f ( sin (4x)) with…

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Q: Find Critical Points and Extreme Values: f(θ) = 2 Sinθ + Cosθ        on [ -2π, 2π ]

A: Given         The critical point is where  f'θ=0              Here the interval is -2π,2π…

Q: In(cos(x)) cos(In(x)) Find the derivative of cos(In(x)) – In(cos(x)) sin(In(x)) A cos (In(x)) -xcos…

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Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: Show that

A: Given: verify that secx=sinxcosx+cosx1+sinx for verifying given identity, we solve left hand side…

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

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Q: e-V2x sinh x sin x x dx

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Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

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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)…

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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: 1+sin x 7. y = in+sin x+ cos.x 8. y = In(In x) 9. sin y = In(x + y) 10. y = log(x sin x) %3D %3D

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Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

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Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

Q: 9) | sin´x-cos'x dx 10) [ cor"/x - dx

A: Solve: 9)  ∫sin4xcos3xdx10) ∫cot2xxdx

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

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Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

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Q: lim as x approaches 0   x sin(x)/1-cos(x)

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Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

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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: 1)f(x)=sin³ 2x 2)f(x) = 4coshr 3)f(x) )= sinx cos*x 4)f(x) = e*cosx 5)f(x) = 8 Inx %3D

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Q: 10. f cos*x sin x dx 11. (sec² 3x) dx / (tan 3x) 12. Setan 2x sec² 2x dx

A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

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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: 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: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

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Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: a) / sin°(x) cos(x) dx = » / sin(x)(cos(x))² dx =

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Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

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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.