Find the solution of the given initial value problem: y (4) + 2y" + y = 9t + 10; y(0) = y'(0) = 0, y″(0) = y(³) (0) = 1. y(t)

Q: Find the following for the given equation. r(t) = (e-t, 5t², 7 tan(t)) (a) r(t) (b) r"(t) = (c) Find…

A: Given: rt = e-t, 5t2, 7 tan t To find: r't , r''t and r'(t)·r''t We know that  ddxex = ex ; ddxtanx…

Q: 1. Given [x² +1, 2x, x ≤ 1 x > 1. Is f differentiable at x = 1? Is it continuous at x = 1?. f(x) =

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Q: @fő)= 5. Find the hypercritical values of the function. f(x) = + x ²² 36x² - 12x² hev's @concup=…

A: Hyper critical values:- those points where the function second derivative is either zero or…

Q: Part C. Find the √√x-5 8). x-15 1 9). +3+ + √x + 10

A: Topic = Function

Q: Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is…

A: Remember that: Time t is taken on x axis and velocity is taken on y axis. The particle moves forward…

Q: A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A: Given that side of the square =90 ft.runs with the speed =27 ft/s.Solution :the distance covered by…

Q: Suppose that a tank with a capacity of 30 gallons initially contains 18 gallons of pure water. A…

A: Concept: Let w(t) be the amount of salt at any time t Now rate of change of w(t) is the difference…

Q: Question 2 Solve the given differential equation (where the function is subject to the given…

A: y'' + 4y' + 29y = 0                 y(0) = 1 and y'(0) = 2let D = differential operator D2y + 4Dy +…

Q: Given that u is a differentiable function, how do we get y' of y = arc csc(u)? T -^= f (x),n. (x),n.…

A: We can solve this as follows:

Q: #1

A: Given query is to solve for separation variable differential equation

Q: Evaluate the integral 10 10 sin(x) cos(x) Note: Use an upper-case "C" for the constant of…

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Q: d. y'= 1+y² 1+t² y(0) = -1

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Q: Evaluate Answer: 5 8 In y [ [³ S 1 1 xy dy dx.

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Q: Find the indicated Midpoint Rule approximation to the following integral. 18 S2x² 2 27 dx using n =…

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Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: answer

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Q: Calculate the flux of the vector field F = (z, x, y) through the surface S which is the portion of…

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Q: Consider the initial value problem Suppose we know that y(t) → 0 as t → ∞. Determine the solution…

A: We need to solve D.E.

Q: Conc.1 Conci .6. Find the intervals where the function concaves upward and concaves down, frx) =…

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Q: [(x² +1) cos +=dx 2

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Q: Question 20 Find the derivative: x²(x² + y²) = y² y = - fo Ov fi P r(2x+y) (1-²) v(22:²-²) x(1+z²)…

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Q: Let y = f(x) = = e -10x ¹+1 Find the equation y = T(x) of the tangent line of the inverse of fat (1,…

A: Given that , y=fx=e-10xx4+1 find the equation of the tangent line of inverse of f at 1,0.

Q: Find the equation of the tangent plane to the graph of z=3x^3+5y^2 at the point above  (x,y)=(1,2).

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Q: 3. Let f(t) = t(1 - 2t). a) Find the average rate of change of f(t) with respect to t as t changes…

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Q: Use the implicit function theorem; dz/dx = -Fpartialx/Fpartialz to find dz/dx and dz/dy…

A: Given expression: ln(2x3+2y6+3z5)= 14+12xyz Let f(x,y,z) = ln(2x3+2y6+3z5)- 14-12xyz We know that…

Q: Find the intercepts of f(x) = −2(x + 2)(x − 5)(x+4) . Enter intercepts as points. If you have more…

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Q: Finally, determine (x³. - x + 8) and simplify the result. Recall that multiplication is commutative…

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Q: Find y' if 7 y² + sin (3x) = 12-y f

A: Here we can find the y' in the below steps, using implicit differentiation.

Q: Obtain the differential equation of this family of curves. The lemniscate ² = acos 20

A: see below the answer and calculation

Q: 2. Find d [ex (x4+1)×] dx J X

A: See this solution in below.

Q: K Find an equation of the tangent line to the curve y ex when x = -2.37. CIXA y= (Simplify your…

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Q: Question 7 Determine the derivative of the given function: y = x² e-* Oy=x²e-e* (2x) Oy = 2² +22 Oy…

A: The given function is; y=x2e-x.

Q: Find the indefinite integral using the substitution x = 2 sin 0. (Remember to use absolute values…

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Q: (a) Write the integration (b) Evaluate the indefin i. ii. iii.

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Q: d Perform the following Operations on the | 14 = (-2₁-3₁-5), V = (4₁-2₁-1) to W² = (-404) R₁W = [ (u…

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Q: How do you get the exponent of 1.67?

A: Given solution :

Q: Solve the equation with homogeneous coefficients. (x² + 3xy + y²)dx - x² dy=0

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Q: Evaluate the following integral using partial fraction decomposition. S 12 (x-4)(x+8) 12 (x-4)(x+8)…

A: The given integral ∫12x-4x+8dx We have to find the integral using partial fraction.

Q: Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least…

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Q: 1) Suppose that F(x) = 15x³+4x² - 3x + π. For each of the following questions, type yes if the…

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Q: Please resolve this one.

A: Given integral:- ∫07dxx+13+1

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: y 4 H…

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Q: f(x) || = ex 1 - ex

A: ddxex1-ex

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y': || y…

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 5x (x -…

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Q: Calculate the integral of f(x, y) = 4x over the region D bounded above by y = x(2 - x) and below by…

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Q: Find the derivative of: Ř(t) = (sin² (3t + 1), ln(t² − 1), ²+1 –

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Q: Classify the following DE's as Exact, Non-exact, Homogeneous or Bernoulli. A: (-xysinx + 2ycosx) dx…

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Q: Question 10 Determine the derivative of the given function y = log(a+b) cosh (2³) where a an…

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 3x…

A: Topic -Partial fraction decomposition We are given, 3x(x-1)2(x2+3)