Find the general solution of the given higher-order differential equatio y(4) + у" + y" %3D 0 y(x) %D

Q: Use the union rule to answer the question. If ​n(A)=8​, ​n(B)=9​, and ​n(A∩​B)=4​, what is ​n(A∪​B)?

A: Formula: n(A∪B) = n(A)+n(B)-n(A∩B)

Q: GIVEN : 2x 2х - 2x ) + 6 1 1 f (x) = 1 --x 8 g(x) = 3(x + + 4 h(x) = 6 - || 3 a.lim -4 · f (x) d.lim…

A: For (a),     limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3

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Q: Solve the initial value problem below using the method of Laplace transforms. y" + 9y = 18t - 18t…

A: Let's find.

Q: 0. 21XVX2 + 1 dx = 142 7, what is | 21uVu? + 1 du? Given that %3D 1

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Q: 4. The function g(t) = (8t)' – cosh² t + sinh t satisfies g'(c) = 0 for which value of c? (a) c= 0…

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Q: True or false If f’(x) = 0 and f”(x) < 0, then the point (x,f(x)) is a local minimum

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Q: Consider the following higher-order differential equation. d³u d?u + - 2u = 0 dt3 dt2 Find all the…

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Q: Evaluate the definite integral. Use a graphing utility to verify your results. 25 dx

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Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

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Q: 3. [3x*(Cos x² + 6)

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Q: 7.3z =0.001 to estimate the slope of the Let f(r) = tangent line at z = 7. 8.1r. Use the difference…

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Q: Adx + (x-y+2)²dy = 0 %3D

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Q: Find Duf at P. f(x, y, z) = 6x³yz?; P(2, –2, 2); u =

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 10 8x + 7 dx

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Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: lim (e2x – 1)* X→0+ Find the limit using L 'Honital's RI

A: We have to find the limit by using L 'Hopital' Rule Rule

Q: Instructions: (1) Use Limit Laws to find the limit of each given problem. (II) You may only use…

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