The inverse of 3 - - 4 x + 1 g (x) = | is . ... 3 + 1 x – 4 –1 g (x) = 3 -1 g (x) x + 4 g' (x) = 3 (x + 4) – 1 g" (x) = -4 x + 1 – 4 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: Evaluating a Function In Exercises 31–34, completethe table.

A: Function: 31. f(x)=-x2+5f(-2)=-(-2)2+5 f(-2)=1f(-1)=-(-1)2+5…

Q: 2.(Trivial) Verify that for any positive integer n the piecewise defined function x2n+1. – x2n+1. x…

A: y = x2n+1, x&lt;0andy'=(2n+1)x2n+1-1y'=(2n+1)x2nVerifying;xy'-(2n+1)y=0L.H.S.=x (2n+1) x2n -(2n+1)…

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: 1.Find the roots of the equation f(x) = x³ - x - 1 using xo 1 %3D %3D For 4 iteration by fixed…

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Q: What do you mean by Polynomial Differential Operators?

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Q: (6) Find a differential equation whose fundamental set of solutions is the given pair of functions:…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 5) Solve xy' + y[1 – In(xy)] = 0 by using a suitable substitution in terms of x and y.

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Q: Using the operators obtained above, obtain the differential equations provided by only the functions…

A: Given : u'(x)+v'(x)-2u(x)-v(x)=0-2u'(x)-v'(x)+u(x)=0

Q: Suppose  is a linear differential operator that factors but has variable coefficients. Do the…

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Q: The function h(x) given by h(x) = –6 – 8.2944x - 4/5x + 3.84x³ has a critical number c = = -1.2.

A: We have given function hx=-6-8.2944x-45x5+3.84x3 and critical number c=-1.2

Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

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

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Q: dt ·S₂ (²+1)' 17.

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Q: x2 dx (x– 1)3 1 In|x-1|- X-1 + C 2(x– 1)? 2 In|x-1| 1 +C 2(x – 1)2 X-1 2 In|x-1|- X-1 1 O Inlx- +C…

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Q: x2n+1 El-1)"; 2n +1 n=0

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Q: Find the particular solution that satisfies the differential equation and the initial condition. f…

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Q: Estimate the value of E-2 (1/(n² + 4)) to within 0.1 of its exact value.

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Q: -0.01 | -0.001 || -0.0001 0.0001 0.001 0.01 x+1, x0 x= 0 ?

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Q: Question (1)  Prove , ez1/ez2  = ez1-z2

A: The given equation is: ez1ez2=ez1-z2

Q: Find the definite integral from 3 to 5 of x+2 / (x^2 - 2x) using partial fraction decomposition

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Q: Given 1/3 ≤ x < y ≤ 3, prove that |ln y − ln x| ≤ 3|y − x|

A: Consider the given inequality ln y-ln x≤3y-x, 13≤x&lt;y≤3 Consider x=12, y=1 Then ln 1-ln…

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: 1. The following table shows the number of absences and grades of 2 students in a Differential…

A: The objective is to compute r i.e correlation coefficient and to determine grades in differential…

Q: What is the coefficient of x^n for the generating function (1)/(1+x)^2?

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Q: 9. X = X= [X1 ; X2] Initial condition X¡(0)=0, X2(0) = 1

A: Given system is X' = 1411 X + 10 e-t Initial condition:- X1 0=0, X2 0=1

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: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y- C

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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: Solve for the exact value of x.x. 4\ln(5x+1)+3=4ln(5x+1)+3=15

A: Given query is to find the value of x.

Q: -3-2-1 -1 543-2 -2 -3 -3 O g(z) = (x + 1)² – 2 O g(2) = (x – 2)² – 1 O g(z) = (x – 1)² + 2 O g(x) =…

A: We have in first figure that function f(x) of y=x2  which translated one unit downwards and two…

Q: 1 3 4 f(x) f(x) -1 -3 -1 1 4 -8 9- -2 -4 Find the following: (z)]" at x-0 Do not enter fractions.…

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Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

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Q: For y = In (x + 3x – - 9), to find y' would require the chain rule. If y = f(g(x)), find an f(x) and…

A: We have to find the derivative using chain rule

Q: 2. Prove that the equation e + x° 0 has exactly one solution.

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Q: (x+1)(x-2) 28. f(x) = %3D o(x-2)(x+2)2 ald worl m1 30. f(x) = O 2+3x %3D %3D 4* - 6(2*) +5 32. f(x)…

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Q: A differential equation is said to be exact when ∂M/∂x=∂N/∂y where M and N are its corresponding…

A: Consider the following differential equation: 3x2y-lnx+3ydx-2lnx+xy-3dy=0 M=-2lnx+xy-3N=3x2y-lnx+3y

Q: Consider f(x) = x^7 + 2x^4-1, 0 = 1. Integrate f over the given interval of x, using Newton Open…

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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…

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Q: x2-1 7) lím x--1 x+1 (x+4)ln(x+6) 8) lím x--4 9) lím x-0 Vx+5-V5 x2-16

A: Compute the limit as follows. limx→-1x2-1x+1=limx→-1x2-12x+1=limx→-1x+1x-1x+1…

Q: Simplification of In x + In(x + 1) = 0 is Ox2 + x-1= 0; x > 0 Ox2 +x +1%= 0; x > 0 %3D x2 +x-e = 0;…

A: Given: ln(x)+ln(x+1)=0

Q: Find y''of 4cos(x/2)+e^-2x

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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: A differential equation is considered to be ordinary if it has more than one independent variable.…

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Q: We conclude that: for every additional distress input, the brain activity increases by 0.061 units…

A: Answer:----.               Date:----6/10/2021 since slope is change in dependent variable with 1…

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

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Q: If the existence theorem is true but the existence and the unity theorem are not, then there is no…

A: Introduction:By using the principles of existence theorem and existence and unity theorem we can…

Q: The function f(x) = (6x+5)e^4x has one critical number. X= ?

A: Proceed as shown below...