2((q–1)u+1) u(1+2u+(q–1)u²) log((q-1)((q-1)²u+2u–1)) u? > 0 for u > Show that [0, 1], q > 3

Q: 0, 0<x<1/n, fn(x) = { /n, 1/n < x < 2/n, 2/n < x<1. 0,

A: Pointwise convergent:- A sequence of function is pointwise convergent, if its every point sequence…

Q: Consider the first order differential equation (ODE) y + For the initial condition y(13) = -2.1,…

A:

Q: The functions {1, x, e3*} are solutions to the differential equation y" - 3y" = 0. Use the ronskian…

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Q: 21 Solve in terms of Besselis Function, 2 11 the ODE: x² + xy + (x³²+ =)=0 let Z=Lnx

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Q: on Technique v = yl-n Substitution Technique v = x1-n

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Q: a+, 3. f(1)=1** +a cosh /21 +bsinh /21 f(1) =2cos" (21) +e² 4.

A: The Laplace transform of the function f(t) is defined as Lf(t)=∫0∞e-stf(t)dt, since the dimension of…

Q: 552 – 4 I(x)= £2 + 1 |1 – 45| 12 – 1,000 f(x) = 5 4r2 – 6 1– 452 m(x)= |4s – 1| g(x)= -4 g3 – s2 + 4…

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Q: 11) Given that iog, 6= m and log, 5 =n, show that log, 10 = mn+m-1 %3D 12) Solve for x in the…

A: Given that  (i) y log2 8 = x and 2x + 8y = 8192 (ii) log2x + 2log4y = 4 and x +12y = 52 Here we have…

Q: Let X1,..., Xn be iid pdf (log(æ)-®1)² 262 1 f(x) -00 < x < o0, and unknown parameters 01 and 02.…

A: Let X1,X2, X3...be iid with pdf, f(x)=1x2πθ2e-(log(x)-θ1)22 θ2          -∞&lt;x&lt;∞   The…

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

A:

Q: Example 15:Form the partial differential equation by eliminating the arbitrary functions f and g…

A:

Q: If x'8, 18 = y" 12 18 = Z ', prove that 3,3 log, x, 3log, y,7 log, z from an A.P. %3D

A: Given:-  If x18=y12=z18,  To Prove:-   3logyx, 3logzy, 7logxz from an A.P.

Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3

A:

Q: 1. Find for y = In () (A)+ 1 3x-2 X-1 1 x-1-x2 (B) x2 - -- x-1 x (х-1) x2 x2(x-1) x-1 1 X-2 (D) (E )…

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Q: 4х- 24 2. f(x) = %D 2x-4 x-int: VA: НА: Hole: Domain: Range:

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Q: e -1 Compute Lt v1+x-1

A:

Q: There is considerable evidence to support the theory that for some species there is a minimum…

A: The logistic model is given by the below differential equation. dPdt=kP1−PM1−mP

Q: log, x = 5.3 and log3 y = 2.1, %3D log4 u = 3.2 and log4 v = 1.3. 19. log3 (9xy) 27. log3 (x²y³) 20.…

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Q: 10.2.2 Use a cobweb to show that x* =0 is globally stable for 0<r< Tin the 1 logistic map.

A: As per the question we have to construct the cobweb diagram for the logistics map : xn+1 = rxn(1-xn)…

Q: 4. Consider the logistic map f(x) = (1+ v6)x(1 – x) • Find the fixed point of 2-periodic cycle. •…

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Q: Verify that each given function is a solution of the given differential equation. Throughout these…

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Q: Example 8 : Form the differential equation by eliminating the arbitrary function ƒ fromn xyz = f (x2…

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Q: Example 8.25. Evaluate x + 2x + 1 Jo 1+ (x + 1)². dx by Gaussian 3-point formula.

A: Gaussian 3-point formula. variable change x=a+b2+b−a2v if ∫abg(x) dx=b-a2∫-11g(a+b2+b-a2v)…

Q: 10x1 + 2x2 + x3 = 13 X1 + 10x2 + 2x3 = 13 2x1 + x2 + 10x3 = 13 What is the (x1,x2, X3) values by…

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Q: Find 2-th and 3-th iteration of the secant method for Ax) = x - x3 + x - 5 Xo = 2, x, = 1 20 15 10…

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Q: 4) To find the root of the equation x² - 3 = 0 using the fixed point method in [1,2], one of the…

A: The given problem is to find the iteration formula for finding the root of the given equation x2-3=0…

Q: Calculate the residue of eZ.e-5=0

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Q: Solve of differential equations by the Laplace transform -2t x' - 5x -e ", x(0) = 3 %3| | |

A: The solution of the given differential equation using laplace transform is solved below.

Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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Q: Find g' (3) . g(x) : In(1+t) dt O In(10) O 6ln(10) O In(4) O 3

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Q: 1.)Integrate: ∫(x+1)(x+2)^6dx Group of answer choices a.)(2/56) (7x + 6)(x + 2)7 + C b.)(2/56)…

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Q: USING ELGEN VALUE x' SOLve EIGEN VECIOR 2'

A:

Q: 6. The equation x² + ax +b = 0, has two real roots a and ß. Show that the iteration method -(axx+b)…

A: The given problem is to the condition for the iteration method convergence near x=α. Given equation…

Q: solve for x if CDy=4(x-E)

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Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

A:

Q: 2) Two strains of bacteria are growing in seperate petri dishes. Intitially, there are strain A 300…

A: the general form of bacteria growth rate is PA(t) = Cabt where,  C is the initial bacteria present…

Q: Solve of differential equations by the Laplace transform x' – 5x -2t = -e ", x(0) = 3 |

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Q: There is considerable evidence to support the theory that for some species there is a minimum…

A: Given fiffrential equation is, dPdt=kp1-PK1-mP Substituting k=0.05, K=10000 and m=500 into the given…

Q: −x^2+x+6 has root(s) at x=

A: To find the roots of the given equation.

Q: construct a first-order linear differential equation whose solutions have the required behavior as t…

A: Consider y=f(t)+3we have to choose some function f(t) such that f(t)→0 as t→+∞, for example…

Q: The Black-Scholes equation is an application of the parabolic partial differential equation (PDE)…

A: Given: To drive the explicit finite difference parabolic equation: ∂V∂t = δ2∂2V2 ∂s2  Here, V = V…

Q: Example 8.19. Use Romberg's method to compute dx 1 + x² correct to 4 decimal places.

A: Let y = 11+x2  and let I = ∫01dx1+x2take h = 0.5 =12The tabulated values of y are   x0 x1 x2 x…

Q: In a simple electric circuit, Ohm's law states that V=IRV=IR, where V is the voltage in volts, I is…

A: Application of derivatives

Q: (a) Show that P(10000 – P) p 10000 – P' (b) Hence, solve the differential equation to show that…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: Specify c_1, co, C and p such that the formula c_1u(8 - h) + cou(s) + cu(s+h) hP u (s) 2 denotes the…

A:

Q: 1. Solve one real root of e - 2x – 5 = 0 with æo = -2 using the Fixed-Point | Iteration Method…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

A:

Q: e-1 : Compute Lt 1+x-1,

A:

Q: 29. Solve the following system of equations. Give exact solutions, not decimal approximations! S In…

A: To solve the given logarithmic equation.

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.