al value problem. E'(t) [6 -3 x(0) = [61 %3D [2 1

Q: Part 1 1. If f(0) = g(0) = 0 and f" and g" are continuous, show that ff f(x)g"(x)dx= f(a)g'(a) — ƒ…

A: I have given the answer in the next step. Hope you understand that

Q: 12. f(x) = 3x4 + 4x³ – 36x², on the intervals %3D (a) [-5,5] (b) [-2, 2] (c) (-3, 1] (d) (-1,3)

A: 12 fx=3x4+4x3-36x2 ⇒f'x=12x3+12x2-72x            =12xx2+x-6            =12xx2+3x-2x-6…

Q: If [f (x)dx=-17 and [f(x)dx=-4, what is the value of [f (x)dx? of f `„S(x)d? O -34 O -13 O 13 O -21

A: Given query is to find the value of indicated integral.

Q: (a) Show that Ye(x) = Ce¯[ P(x)dx

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Q: y aln(a) – y = 0; y(2) = In(4)

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Q: Find an equation of the line tangent to the graph of G(x) = 4 e - 7x at the point (0,4).

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Q: Find a formula for f(") (x) if f(x) = e-10: fln)(z) =[]

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Q: 4. If fdx = f(x)[In(x) + 1] + C, then f(1) =

A: We have, ∫lnxx2dx = fxlnx+1+C To evaluate : The value of f1

Q: 54. f(x) = 3 – 2x² +x³, [a, b] = [-1,1] %3D

A: Given. 54) f(x)=3-2x2+x3,[a,b]=[-1,1]

Q: 1 g(x) (1 – x)3'

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Q: (3) Let X = n(µ,4) and Var(2x) = E(4-7x) find u.

A: Given,X~n(μ , 4)

Q: If f(3) = 5, f'(3) = 5, g(3) = 1 and gʻ(3) = 1, then z f(z) g(z) dr

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Q: Question 30 Determine the second derivative of 2x³ + y²= 1 – 4 y A 6x ( y + 2)-! - 9xª ( y + 2 ) -3…

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Q: 6. Suppose h(r) = (f(r) + VT) · g(r), f(4) = 3, g(4) = -1, and f'(4) = g'(4) = 5. What is h'(4)?…

A: Given h(x) = (f(x)+x )·g(x)h'(x) = d( (f(x)+x )·g(x))dx

Q: Suppose the function V represents the number of people vaccinated for COVID-19 in Kalamazoo country.…

A: Given that the function V(t) represents the number of people vaccinated for COVID-19

Q: A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 inches, a…

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Q: If f, g L₂ then [S* S(x)g (x) dx ] * ≤ [f*° ƒ^²(x)dx ] [1° g² (x) dx]

A: This is the famous Cauchy Schwarz inequality for integrals. It follows by working with quadratic…

Q: Find dy/dx by implicit differentiation. x3 + x2y + 7y2 = 4 %3D y' = %3D

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Q: Show that esin(x²)dx < e– 1.

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Q: QUESTION 8 If then the value of y' is 3cosx - 10 3sinx - 10 3cosx + 10

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Q: Question 1 Consider the following table of values: X f(x) f'(x) g(x) g'(x) -2 -3 1 2 3 4 -5-6-7 Find…

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Q: Question 3 Suppose that f satisfies | f(x) dx = 6 and 1| f(x)dx= –4. Calculate -5 (2.x + 10 – f(x))…

A: Given that: ∫-53f(x)dx=6 and ∫35f(x)dx=-4

Q: Problem #5: Let f(x) = 2. Which of the following is equal to f'()? %3D 5. (i) lim 40+h 4. 40 (ii)…

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Q: Г. 5 1, г)ах — 9, g(x)dx 8 Compute: -[о g(x)dx b.) == 5 3f(х)dx %— с.) .5 f(x)dx d.) 2 "/Г 5…

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Q: x2 + 2 -dx. | (* – 1)(x – 4)(x+2)

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Q: g (x) = V2x-1- 1. Which function is the inverse of of (x) = 2(x+ 1)° + 1 of (x) = 2 (z+1)3 +1 ° f…

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Q: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x .…

Q: Approximating the shaded area with the (a) Trapezoidal rule and a step size of h=1 yields square…

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Q: You deposit $2000 in an account with an annual interest rate of r (in decimal form) compounded…

A: Please refer to the solution in next step.

Q: 1) Find the equation of the curve whose slope at any point p(x.y) is m = (x+16x +4)(x+4) and passing…

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Q: 1 (x2 5)e-X dx

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Q: (a) Find the first and second derivatives of the following function (1² + x)(x² – x + 1) f(x) = %3D…

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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.