b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

Q: s sec(cosx) dydx siny

A: Given : ∫01∫sin-1yπ2 sec2(cosx)dydx

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

A:

Q: Find the intergration of x^3(x^4-sine)^5 dx

A:

Q: Prove the formula.

A: Given a function Arc Sine Hyperbolic (t). We need to find the derivative of the function. Let's…

Q: test for the exactness of the differentral dy + Cosx +Sinyfy -0 quation And hence find the Salution…

A: A differential equation contains independent variables, dependent variables, and the differential…

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: Compute for a real root of 2 cos x – sin vx = i accurate to 4 significant figures using Fixed-Point…

A: 2cosx3-sinx=14  compute for a real root of equation using fixed point iteration method with an…

Q: Resolver por transformada de laplace  Y"+4y=cosx.  Y(0)=1  y'(0)=1

A:

Q: b,c,d

A:

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: solve the IVP x(1-siny)dy=(cosx-cosy-y)dx y(π/2) =0

A:

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

A:

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x)+ 4)dx must be transformed into using suitable…

A:

Q: -siny(x + siny)dx + 2x²cosydy = 0 %3D

A:

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: zy (Smxa CosX) Axー Sinhy

A:

Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

A:

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

A:

Q: dy cosx+ ysin x =1 dx

A:

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

A:

Q: = Solve: Cony siny dx + dy. cosr sinx

A:

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

A:

Q: Solve x - cos(x) = 0 by Secant method. Use x-1 = 0.5 and xo = 1.0 as the initial estimates. %3D

A: We will find roots till 4 digit repeat

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

A:

Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: Find dy/dx of x siny + y = 4x + 3

A:

Q: y = Arctan ( sinh (2x)); y' = * O - 2 coshx /(1+ sinh^2 (2x)) O 2 coshx / (1+ sinh^2 (2x)) O 2/ cosh…

A:

Q: Siny dx t sin Zydy + x dy

A: To solve: sin⁡ydx+sin2⁡ydy+xdy=0…

Q: Calculate •3 2x -dx et – 1 - -3 by Gaussian quadrature with n = 3.

A:

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

A:

Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

A:

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

Q: Compute for a real root of 1 2 cos Vx – sin vx = accurate to 4 | 4 significant figures using…

A: 2cos(33)-sinx=14;   x0=π f(x)=2cos(33)-sinx-14 f(x)=0 ⇒2cos(33)-sinx-14=0 x=cos-11214+sinx3=ϕ(x);…

Q: Find dy/dt Y=(1+Sin 12t)^-5

A: Given function is y=(1+sin12t)-5

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.