For each ODE with non-constant coefficients, use the given homogenous solution to find a particular solution by variation of parameters.

Q: Find numbers a and b, or k, so that f is continuous at every point. 3x+ 9, if x<-6 f(x) = { kx+ 6,…

A: Hair we are given that the function is continuous at every point. we use the concept of limit for…

Q: An object attached to a spring oscillates around a position and is represented by the function…

A: Substitute value of 1 in y and solve for x.

Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: Find the intervals on which the function is continuous. x +5 17) y =2-7x + 10

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Q: Does the MVT apply to f(x) =- x²_3x+5 on the interval [-1, 2]? (x-1)

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Q: (- 0,a) is measurable.

A: Note that, every interval is measurable.

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4e* on the interval [0,…

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Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: The area bounded by the curve y 7x and the lines x = 9 and x = 42 above the x х — ахis - is_ O…

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Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

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Q: If f(x) = 3x — 7, find the image of 2 and the preimage of 2

A: Given: fx=3x-7 To determine: Image &amp; pre-image of 2.

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(0) = 0

A: Given: f(0)=0

Q: f(x) = x2 -4x-2 at x = 1 %3D %3D

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Q: Find the sum of the values of f(x) = x2  over the integers 1,2,3,...,10

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Q: Find the values of a and b that make f continuous every ²-4 If x < 2 f(x) = If 2 ≤ x <3 ax² - bx + 3…

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Q: At what interval of x will the function continuous, f(x) = { 3x²-x-2 x-1 0, x= 1 ", x#1

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Q: Consider the ODE below. x = 2 + x² *y" + x²y" – 6xy' + 6y : %3D - Show complete solution and…

A: The differential equation given is as follows: x3y'''+x2y''-6xy'+6y=2x+x2 Divide both sides of the…

Q: Write the formula of partial derivation with respect to x?

A: Partial derivatives  Let  f(x,y) is a function given , in which f(x,y) partially depends on x and y,…

Q: Find the constant a such that the function is continuous on the entire real line. 9x², ax - 3, a = x…

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Q: Find a power function of the form y = axp going through the points (1, 6) and (8, 252).

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Q: Solve for a and b that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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Q: express the set of numbers x satisfying the given condition as an interval.       lxl ≤ 9

A: Given: x≤ 9 Express x≤ 9 in terms of interval

Q: Find the first 3 iterates of the function f (x) = 0.75x when 0 = 5. O 5, 3.75, 2.8125 O 3.75,…

A: To get the next iterate, apply the function f(x) to the previous  one.

Q: Determine the interval on which the function f( x) = 44x – 4-x+12 is concave down.

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Q: Graph h and describe the discontinuity: for x 0 Is h left- or right-continuous?

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Q: What is the total change of f(x), if ƒ'(x) = 2x − 3x², over the interval [0, 3 -18 -12 -6

A: Given query is to find the total change for the given intererval.

Q: What is the main condition that makes an ODE homogenous or non-homogenous?

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Q: 5. * y = ( In æ)²

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Q: Differentiate the following f(x) =/20x- sin²(2x) Ox –

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Q: find the ode by eliminating the arbitrary constant

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Q: Find the point on the curve h(x)=x2−8 that is closest to the point (−18,−8). Enter your answer as an…

A: If the point on the curve h(x) = x2 − 8 is closest to the point (−18,−8), then their distance will…

Q: Solve for a andb that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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Q: Graph the function f(x) = 2csc r over a one-period interval.

A: The given data is: fx=2 cosecx      (1) To graph the function over a one-period interval.

Q: Compare the graphs of the functions. Y1 = In(2x) and Y2 = In 2 + In x

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Q: Find the function g such that fog = In (2x° +7) if f(x) = In x g(x) = %3D

A: Find the function g such that  f(g(x))= ln(2x3+7) and f(x) = ln(x) .

Q: Show that div (r x a) = 0

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Q: Find a power function of the form y = axp going through the points (1, 6) and (8, 252

A: To find the power function for the given form.

Q: Use f (x) = -2 In(x + 1) to do the following: %3D

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Q: Find its x co-ordinate.

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Q: Find the first 3 Iterates of the function f(x) = - 2x + 3 when x 3 =0 . 3, - 3, 9 - 2, 0, 2 2 z, -…

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Q: Find the values of a and b that makef continuous everywh x2 – 4 - if x 3 a = b =

A: A function f is continuous when x=c is the same as saying that the function's two-side limit at x=c…

Q: exists depends on as long as tť? <

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Q: (- 0 ,a) is measurable .

A: Given a statement

Q: ) Show that |2x - 2|-|x+1| +2≥0 for every x € R.

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Q: hraj h(x) = 3x-2 x347

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Q: Which of the following functions passes through the point (0,12) and satisfies f'(x)=8 ?

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Q: Find the root(s) of f(x) = x-12.42x +50.444x-66.552 in the interval 4sx56 to accuracy of 0.001.

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Q: Derive a formula for the absolute error of a quotient X2

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Q: Q: A- find for the functions: - In =) + In(3x2) = In(3) %3!

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.