(a) if f (t) = tet cos 5t then L{f (t)} =?.

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

A:

Q: Example 2.34. Apply Muller's method to find the root of the equation cos x = xe which lies between 0…

A: Here we need to use muller's methode.

Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2…

A:

Q: 1. Solve the initial value problem: dy 2xy): 1 + cos x y(y + sin x), y(0) = 1. dx %3D 1+ y?

A: The given differential equation is  11+y2+cosx-2xydydx=yy+sinx,  y(0)=1

Q: 3. Solve the following initial condition problems a. f'(x) = sin(2x)+ cos(3x), f(0) = 5 b. g"(x) =…

A:

Q: Find the function f(x) described by the given initial value problem. F'(x)=sin x , f(0)=-3

A:

Q: Example 10.14. Apply Runge's method to find an approximate value of y when x= 0.2, given that dy/dx…

A:

Q: If the function f (x) solves the initial value problem dy E (х + 1)-И dx -1/2 IT • cos(TX)

A: Givendydx=x+1-1/2-πcos(πx)

Q: Find a linear differential operator that annihilates the given function. 2.3 + e* cos 2x

A: Let, the given function:fx=3+excos 2x

Q: By using first fundamental theorem of calculus. Solve the problem 1.) Suppose f(x, y) = S*3 If fx…

A:

Q: b. Solve the initial value problem: f (x)= sin x +e2, f(0) = 4 1 f (0) 2

A: Given: f''(x) = sin x + e2x, f(0) = 14 and f'(0) =12

Q: f'(x) = cos x; y (G) = 3 %3D

A:

Q: Construct a first-order linear ordinary differential equation so that all solutions are asymptotic…

A: Given the function                     f(t)=1+t+t2

Q: Q4 B) Find y' for the functions cos(xy) + 3*+cos ly+ In(xy) + log-7 dy

A:

Q: If the function f (x) solves the initial value problem dy = (x +1)-1/2 – T · cos(T2) y(3) = 2 , %3D…

A: Given: dydx=x+1-12-π·cosπx Now separate the variables; dy=x+1-12-π·cosπxdx Now taking integral on…

Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

A:

Q: A particle moves along the x-axis with position given by x (t) = -2 cos (2t) + 2 for time t > 0.…

A:

Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

A:

Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

A:

Q: Find a linear differential operator that annihilate the given function d) Sin5x + 10 cos5x e)…

A: (d) Given that y=sin5x+10cos5x We have to find a linear differential operator that annihilate the…

Q: determine the annihilator of the givenfunction. F(x) = x cos 3x.

A: Consider the given function, F(x) =x*cos 3x. Let f(x) is a function, which is defined as,…

Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 2 cos 5x. a2. - 00 0, u(x,0)…

A:

Q: 1. S8te7 dt 2. "(1 – 3x) sin Gx) dx -2n L w²e*wdw 3.

A: Given, Simplify

Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

A:

Q: 1. Find a differential operator that annihilates the function xe2 ( cos 3x + 3).

A: Given problem is :

Q: 1) The value of f t.e-3t. sin 2t dt

A:

Q: :- x2 + 10x + 24 dx. 1+ cos2 (x) f(t) = %3D At what value of t does the local max of f(t) occur? t =

A: Given: ft=∫0tx2+10x+241+cos2xdx

Q: 2. Solve the initial value problem f"(x)= 2cosec3xcot3x +5 cos(-x)+3, given Зл = 4 4

A:

Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

A:

Q: 1 1. The function Y = sin(t² )+ 4 is graphed below. Define F(x) = [, sin(1²) + - 1 dt 4

A: Given: F(x)=∫0xsint2+14dtThus, Fx represents the area under the curve y=sint2+14(a) First of all we…

Q: Solve the initial value problem.

A: To solve the initial value problem.

Q: In 1 & 2 find dz/dx by the chain rule and also by rewriting z. 2 = (3x) z = /1- cos?x 1. 2.

A: Let's find.

Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: Solve the initial value problem: f'(x)= cosx + sec2(x), f(pi/4)= 2 + ((√2)/2)

A: We have to solve the initial value problem where, f'x=cosx+sec2x and fπ4=2+22 Integrating both sides…

Q: Solve the initial value problem. dy + y sin x = 2x cos² x, dx y(0) = 0 COS X - 2.

A: Given: cos(x)dydx+y sin(x)=2x cos2(x)

Q: 1. [8te" dt 2. . (1–3x)sin(}x)dx 3. w'e*™ dw 1-1

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

Q: ds Find the particular solution of dt H|2 1 = cos-t

A: The given equation is;  ds/dt = cos (t/2).

Q: 1) Se2t cos(e') dt

A: Consider the integral  ∫e2tcosetdt

Q: Solve the initial value problem: dx/dt+2x=cos(5t) with x(0)=5 find x(t)

A:

Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

A:

Q: g(x) - Stoc cos (x + t) g(t) dt = 1 [1- (π/2)]

A:

Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

A:

Q: 4. a) Transform the following Cauchy Euler equationto a differential with constant coefficients by…

A:

Q: 1. f(t) = cos(6t) 2. f(t) = (e^(8t)) cosh(3t) 3. f(t) = (t^2) e^(-4t)

A: Lcos(at)=ss2+a2 Leatcosh (bt) = s-a(s-a)2-b2 Ltneat = n!s-an+1

Q: QUESTION 4 Given f(x) = 8x³ + 2x. Estimate the value of ƒ(2.01) using differential. %3D

A:

Q: Example 6.1 Express the following differential equation as an algebraic equation using the Laplace…

A: Given differential equation is x"(t)+x'(t)+x(t)=1

Q: Solve the initial value problem dx/dt+2x=cos(3t) with x(0)=−1.

A: This is a first order linear Ordinary Differential Equation of the form x't+ptx=qt Integrating…

Q: 8. Solve the initial value problem: ( dy = y(y + sin x), y(0) = 1 dx + cos x – + y? 2xy

A: The given problem is to solve the given initial value problem, Firstly we have to check the…

Q: Find the general solution of (x + y) cos ydr + (a cos y - sin y)dy = 0. |3|

A: Differential Equation: A differential equation is an equation that contains one or more terms and…

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.