r = 2 – 2V2 cos 0

Q: 3 (b) / 2³ x³ cos(x¹ + 2) dx

A:

Q: 2. f(1) =t cos8t +2

A:

Q: 8 +10x-32+x? cos 2x 4 Find : (a) y = %3D x2

A: Given y we have to find dy/dx as shown below

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: -3x cos(x) + C2 e ,-3x ¯ 3" sin(a + c2xeš* -2x + c2 e2a * + C2xe-2

A: Given : The given equation is  9y" - 6y + y = 0

Q: 2sin 0 d0 2+cos 0 (2+cos 0)²,

A: Given integral is∫02π22+cosθ2+2sinθ2+cosθ22dθ

Q: 14-f(t)= cos 2t.

A:

Q: y" +3y' – 2y = e-2*[(20x + 4) cos 3.x + (-32.x + 26) sin 3.x] |

A:

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: de cos² 0

A:

Q: 3) v = C,e2x cos 3x + Ce sin 3x 2x

A:

Q: 187. [T] f (x) =1+ cosr, x = 3元 2. COS I,

A: Given: fx=1+cosx The tangent line is to be found at, x=3π2

Q: Use undetermined coefficients method to solve b. y" – 2y' + 5y = e* cos 2x %3D

A:

Q: Evaluate [em 2* cos 2.x dx a) 2esin 2x +c cos 2x e b) c) ecos2x +c sin 2x d) –+C

A:

Q: (c) y= sv1– s-1 + cos¯'(s)

A: To find the derivative of the given function

Q: 2/2 16/1+cos 0 de 0

A: We use the half-angle identity

Q: 3 Find ALL solutions of cos 2x = 2 %3D

A:

Q: V3 11. cos(3x) = %3D

A: cosθ   is negative in 2nd and 3rd quadrant

Q: xcosx dc + Cos x da 2.

A:

Q: Solve y" – 9y = (x² + 5) cos x. Use the superposition approach.

A: y"-9y=(x2+5)cosx      ...(1)the auxillary equation of the differential equation m2-9=0⇒m=±3…

Q: r=2 Sin cQ-Ę) Cos co-Ę)

A: The given equation is r=2sinθ-π4cosθ-π4 Apply the formula sin2θ=2sinθcosθ to get:…

Q: #+2 Q.23) cos²3x dx = 24 a)- #+24 KT -24

A:

Q: 5. Find (b) y = cos (11x + 5x).

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Q: ∫0pi cos2t*cos4t dt

A:

Q: Find the value of A. (A – B + C) + (2A + B) sin (2y) – (2B – A) cos (2y) = (4 + j3) – (6 – j2)…

A: Given,

Q: What is the value of csc ( 1) 137 7T + cos( V3+2/2 O -V3-2/2 -V3+2/2 2 V3-2/2

A:

Q: T 1-sin 0 A) [ ] p2 cos 0 drd0 0 0

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

Q: 3. cos 20 de –2p cos 8+p2 , p| < 1 [). 2np2

A:

Q: fCx) at c0,2) で +x + co.2) 2. メ 2/3

A: Given curve is fx=23x2+x+2. To find the equation of tangent line and normal line of the curve at…

Q: Σ Σ cos C. n = 1 2n2 – 1 |

A: The objective is to find the sum of the series.

Q: 8. y"+y = 3 cos 2.xr,

A:

Q: 5. Find (b) y = cos (11xs+ 5x).

A:

Q: Find all solutions in{ 0, 2m): cos² z – cos z=0

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Q: (D² – 4D + 3)y = 20 cos x

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Q: 5. y = c1 cos 2x + c2 sin 2r; y" + 4y = 0

A:

Q: (cos(3x)(/1 – c os(5æ))dæ -

A: Use the formula 2cosA sinB = sin(A+B)-sin(A-B)

Q: "+2y + 5y = 6 sin 2r +7 cos 2r

A: Given that y''+2y'+5y=6sin2x+7cos2x The objective is to solve the equation, Now let's consider…

Q: '(s) (c) y= sv1– s+ cos

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

Q: SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п <x< 8п n=1 +

A: The Fourier series of the function fx on -L,L is as follows. fx=a0+∑n=1∞ancosnπxL+bnsinnπxL. Use the…

Q: (5e" + 6x + 5 cos z)da

A: The solution is given below

Q: 2 cos(2x) – V3 = 0.

A: Given  2cos2x -√3=0

Q: . Evaluate [10x cos(x²) dx . A) sin(x³)+C C) 30 sin(x') +C 3 B) sin(x') +C 10 D) 3 sin(x') +C 10

A: Our Aim is to evaluate the integral given below:-∫10 x2 cos (x3) dx -(i)

Q: Test for exactness and find the general solution of: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy…

A: To solve the following differential equation

Q: cos (y) C = 3x2

A:

Q: Solve the equation on the interval 0<0< 2T. cos 20+2 cos 0 + 1 = 0 O A. 4' 4 J T 3n O B. 2' 2 ] OC.…

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Q: cos(3w) (iv) 1+w2

A:

Q: y′ = cos2(x) cos2(2y)

A:

Q: c) Find all solutions of 2cos.xsin 2x - V3 cos x = 0. 5c.

A:

Q: r = sin 0 + 2 cos² 0

A: Given

Q: (2D – 5)y = sin 2x – 7 cos 2x -

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.