Cos ax COs ax Q: Prove that dx = ze", a 2 0.(or) Evaluate x² +1 x² +1

Q: sin (t) -dt 3 (4+ cos (t))?

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Q: 15. y = sec'x, y 8 cos x, -T/3 < x< T/3

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Q: 3 sin z If f(2) = then 2 + cos z f'(2) =| f'(5) -

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Q: cos ne sin no 4.0 |cosh t sinh t |- sin ne cos ne sinh t cosh t

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Q: Q.5/ Show that sin(z) = sin(x) cosh(y) + i cos(x) sinh(y)

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Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

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Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: 2. I t/Cos X SinX

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Q: Q. It sin x Cos X XCOS xQ /- sin xd 3.

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Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: Using Variation of Parameters 4y''+4=cos-1x

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Q: T Cos x-sin x Jr x² dx So

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Q: 3 sin a If f(x) –, then 2+ cos x 3+ 6 cos(x) (2+ cos (z))² f'(x) = f'(5) =

A: For part (b) just put 5 in place of x in the expression of part (a).

Q: f1(x) = sin(x1) cos(x2), T f2(x, y) = xy, f3(x) = xx¹, € R² x = x, yern XER"

A: Given the following functions                  f1(x)=sin(x1)cos(x2),   x∈ℝ2f2(x, y)=xTy,   x, y∈ℝn…

Q: 2z2 cos 5z dz EVALUATE.

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Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

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Q: Q: Evaluate: 2х -1 cos dx (1+x²

A: Solved below

Q: 1+cosx, dr r = 1-cosx' dx

A: Using derivative to find dr/dx

Q: Assuming that y is a function of x, then - (cos(x²)] = -2x sin(x²). dx Assuming that y is a function…

A: Use chain rule of differentiation to differentiate composite functions. ddxfgx=f'gx⋅ddxgx

Q: cOS X sec x = 2 sin x if 0 Sx< 2m А. п/4, Зл/4 В. π/ 3, 5π/3 С. T/6, 5n/6

A: Given: cosxsecx=2sinx

Q: 1 Eliminabe the arbitrary constants C,e"cos 2x - 3X SIn 2x + - ZX Y C,e

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Q: 4 sin"t- cos *t= sint- cos 4 2 2

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Q: (sin 0-2rcos 0) dr + rcos0 (2rsind + 1) d0 = 0, when r = 1; 60=0 %3D

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Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: S cosx. sin“x. dx = cos³x + C sinx + C O None O sin*x 4 + C

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Q: Test the DE for exactness then solve. 6. (2xy³ + cos x tan y + 2 sin x) dx + (3x²y² + sin x sec? y –…

A: As we know that, the differential equation Mdx+Ndy=0 is exact. if  ∂M∂y=∂N∂x The solution of the…

Q: tan( tan3x) dx Evaluate: cos?3x A) 3 -In|sec (tan3x)|+C -In|cos( tan3x)|+C 3 In|cos(tan3x)|+C In|sec…

A: Just I have make the substitution and solved the given integral.

Q: sin If y = show that (1- x²) 1-x -1 x. d'y -3x dy drソミ0 dx? ーy=

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Q: 7/2 #1. cos'x dx | tan*e sec*o de #2. S tan'r sec'r de #3.

A: As per guidelines we are supposed to do only first three questions of a multiple question. To get…

Q: sec x sin x dx 3. J Vcos? x + sec x (Hint: factor out cos² x) .2

A: Given, ∫sec3xsinxdxcos2x+secx

Q: (- x cos r) dz. Evaluate /2

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Q: h(x, y) = cos x coS y. COS x cos

A: Given that h(x,y)=cos(x)cos(y) with |x|&lt;0.1 |y|&lt;0.1 To find the second degree Taylor's…

Q: S sin(ax)cos(ax)/3 – cos(2ax) dx

A: Sin(2ax) = 2*Sin(ax)*Cos(ax)

Q: I sec25x dx = ? tan x +C 1/5 tan x +c 1/5 tan 8x +C

A: We will solve the problem

Q: 1+ sin r , r < 0 f(x) = COs a sin x

A: Now, check the function is continuous at x=0 or not. Thus, the function is continuous at x=0.

Q: (d) r(π/6 + At) - r(π/6) = √3 2 cos At sin Ar-1+(cos Ar i+ At + 2 3√3 2 -sin At 1 3/-)1 2 X

A: We can solve as follows

Q: tinuous, prove that T/2 T/2 f(cos x) dx = f(sin x) dx (b) Use part (a) to evaluate /2 cos?x dx and…

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Q: 2) sec?x tan y dy + sec?y tan x dx 0 Ans: cos 2x+ cos 2y = c

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Q: al Evalluate; I. cos X AX V sin x Hints sin'x+cosX-4

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Q: 2 cos (x) +2cos (x) + 1=0 O A. 4 4. O B. {2x} O C. {t}

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Q: 2 sec? r 1 1 Prove the identity: 1-sin x + 1+sin x

A: This is trignomertric question

Q: f(x) = 2 cos2(x), COS a = 0

A: Given data:       The given function is: f(x)=2 cos2(x). The given value of the constant is:a=0.…

Q: 3 Cos |X TT 13) y = 3

A: We need to plot the graph of given curve:

Q: 2 cos e de 2 V1 – sin 0

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Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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Q: sec x + coOS x dx 2 cos x

A: To evaluate

Q: 6. f(t)=-e* sin ( 21 + 7)

A: As per bartleby guidelines we only give first question answers.