Hiw.r provethat D2f +32f= y=o far the functionel xe -2y Coos 2X %3D

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Q: Find all critical values for the function f(x) = 10x – 30x + 5, and then list them (separated by com...

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Q: Evaluate f (2 cos x-sin x)² sin x

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Q: 4 + 2 -3 -2 -1 3 х X. Figure Q1(d) Find the positive root of f(x)=x²-sin x as shown in Figure Q1(d) ...

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Q: A conical tank of water, 10 ft high with radius of 6 ft, is leaking at the bottom at the rate of 10 ...

A: Given:-for conical tank height,  h0=10 ftradius,  r0=6 ftwater is leaking at the rate of 10 cubic fe...

Q: dx 4+ x² Use integration by parts. let u = x? dx 4+ x2 dv =

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Q: Sx Vx + 10 dx

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Q: Find (e-*) dzdy A. 4ye-(*²+y²) B. 4xe-(2²+y²) C. 4xye-(x²+y²) D. -4xye-(a²+y²) OC OA OB None of the ...

A: Partially differentiate the function y= e-(x2+y2)  w.r.t. x and y . 

Q: 3 (х + у)dx dy 1 0.

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Q: Evaluate the following limits. 1. lim (1+ Vw)(2 – w² + 3w*)

A: According to our company rules we can answer only the first question and rest can be reposted.

Q: f) {1,0,–1,1,0, –1,1,0,...}

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Q: x* + ах — 2bx — 2аb — хз — 2ах* - 2bx? dx х4 + аx3 — 2bx3 - 2аbx?

A: I=-∫ x3+(2b+2a-1)x2+(2b-a)x+2abx2(x2+ax-2bx-2ab)dxI=-∫ x3+(2b+2a-1)x2+(2b-a)x+2abx2(x+a)(x-2b)dxPerf...

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A: Please refer to the image below 

Q: Rewrite exponents as factors using the Power Rule of Logarithms. Do not evaluate the logarithm. logs...

A: Note that, the power rule of Logarithms is: ln xn=n ln x

Q: 2 cos 0 d0 V1 – sin 0

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Q: 出w-2 Verify that Wメy Wyx for the functionss T- f(xsy) = En (2X +34) fcxyy) = e+x Luy +y Lnx 2-

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Q: dx Evaluate J 2/4+x²

A:    ∫1x24+x2dxLet x=2 tan u.=∫secu4tan2udu=14·∫secutan2udu=14·∫cosusin2uduLet v=sin u.=14·∫1v2dv=14-1...

Q: H-wr Phavethat D2 22=o far the funstions far the kunction -2y t- Rx,y) = e Ln JxZ+yZ CooS 2X

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Q: Determine whether the function has an inverse function. Зх + 7 f(x) 7х + 2 Yes, f does have an inver...

A: To find the inverse of a function

Q: Sketch a graph that shows the water level versus time.

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Q: 5. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a ...

A: Given query is to find the speed at which bottom of the ladder is sliding.

Q: ( 2x + y -3z = 0 -2x + 2y + z = -7 3x - 4y-3z %3D %3D 7

A: We have to solve the system of linear equations.

Q: - Trig Sub dx x+V9 – x2

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Q: A rod is sliding down the side of a wall such that the height is decreasing at a rate of 5 inches pe...

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Q: x'y' = 4x? + 7xy + 2y? %3D

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Q: Find the area bounded by y = sin(x) and y = sin*(x) from 0 < x <.

A: Given,             y=sinx , y=sin4x from 0≤x≤π2To find : Find the area bounded by the curves.

Q: 11. A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom,...

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Q: Definite Integral Instruction: Answer the following. Show all your solutions. 3. sin xdx (1 + w)(2w ...

A: As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫sinxdx=-cosx+C   From the given integration; (...

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Q: Consider the fünction: f(x) = 5x + 15x² - 5x- 3 %3D Step 1 of 2: Determine the intervals on which th...

A: Concave up if f"(x)&gt;0 Concave down if f"(x)&lt;0

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotat ab...

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Q: Use the Root Test toO determine if the series (-1)" 2/n Σ CONVERGES en? (2n2 – 1)" n=1 converges or ...

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Q: ind the antiderivative, G(t), of the function g(t) = (2n²t? – t*)v2n² – t2.

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Q: Which of the following equations is an exact DE? O (10x^2 +5)dx-20xydy%3D0 O (2xy-3x^2)dx+(x^2-2y) d...

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Q: Va –2 -dx aㅎ (V+1)

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Q: Explain how to convert (6.3, 3.8) from rectangular coordinates to polar coordinates.

A: Find the magnitude and angle of the point from the positive x-axis.

Q: EVALUATE THE FOLLOWING INTEGRALS: (BY PARTS OR TIC TAC TOE METHOD)

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Q: first prove that ()" <n! < ()" forn2 6.

A: We will prove                        n3n≤n!≤n3n for n≥6.