R X 0 1 e,y = 0, x = 0, andx = In 4; about the x-axis 19. y y 445 yA cross sosceles ertical y= ex R In 4 0 y

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A: We use the chain rule and product rule to find the derivative.

Q: (c) Given that y satisfies the differential cquation (x+1)= 2x- y, dx dy usc the approximation y" y.…

A: 2 (c)  x+1dydx=2x-y⇒dydx=2x-yx+1 h=0.2, y0=1 So, y0=1, x0=0 x1=x0+h⇒x1=0+0.2=0.2 When  y0=1, x0=0,…

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A: use implicit  differenetiation to find the unknown.

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A: Heun's Method: Consider dydx=f(x, y)with y(x0)=y0Thenyn+1=yn+h2(f(xn, yn)+f(xn+1, kn+1)where…

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Q: Find the length of the curve y=x between x = 0 and x= 6. The length of the curve y =x? between x= 0…

A: We have to find the length of curve.

Q: Question 9

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Q: The volume of a right circular cone of radius a and height y is given by V 1 - TXʻy. Suppose that t…

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A: NOTE: Refresh your page if you can't see any equations. . here we have

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Q: The volume of a right circular cone of radius x and height y is given by V = 1 T2ʻy. Suppose that…

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Q: 2 Given z = 2 cost + 30 and y= 5 sin t dt dy dt dy dx %3D %3D

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Q: The volume of a right circular cone of radius x and height y is given by V=1/3πx2y. Suppose that the…

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Q: az az + y dy Ty+z. a) If z= zy- Te. show that x b) The surface area S of a right circular cone of…

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Q: dy = y-x, y(0) = 2, then the value of y(0.2) by using 4th order 8. Given dx Runge-Kutta method…

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Q: 10. The sides of the rectangle at right increase in such a way that the instant when x = 4 and y =…

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Q: • Find so lutions usino Ex act Equations 1.) solve (ysinx t xycosx) dx + (Xsinx + 1)dy=0

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Q: 2) dy 3x-y+1 3y-x+5 Apply homogeneity test to differ en tial equertion cnd solve. %3D

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Q: = T Cos (4), what is the total distance :0 to t = 4? A particle has velocity function v(t) traveled…

A: The objective of the question is determine the total distance from the given velocity function…

Q: The work done 'W' by a gas on a piston is given by P2 W = CP dp Where 'P' is pressure and 'C' is…

A: Given : Work done W = ∫p1p2 CP-1ndp Where P is pressure and C is constant.   To find : Show that…

Q: C: 1- Find for the function: X²+ Siny =X.y² 2- Find the mnd dy por the fur etion - for the fum…

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Q: Create a bucket by rotating around the y axis the curve y = 3 ln(r- 1) from y = 0 to y 10. If this…

A: Given: Create a bucket by rotating around the y-axis the given curve, y=3lnx-1 from y=0 to y=10…

Q: 1 cone of radius x and height y is given by V = =Tx2 y. Suppose that the 3 dy Find when x = 2 and y…

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Q: The following situation applies to the attached question The fluid pressure (in atmospheres) at the…

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Q: 1 3. y 4. 9. dy at x=5 using Newton's divided difference formula. dx Find the value of

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Q: i) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…

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Q: dy For = 4x/7+ y? and y(0) = 2, use Euler's method with h = 0.1 to approximate y(0.5). dx…

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Q: 1 The volume of a right circular cone of radius x and height y is given by V = Txʻy. Suppose that…

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Q: dV when r = 7 and dt An expanding sphere has radius r = 0.4t cm at time t (in seconds). Let V be the…

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Q: Use Euler's Method to approximate y(10.8) with step sizeh 0.2. dy = 3y + x- 5 y(10)= 0 %3D dx

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Q: dy = xy + eX, y(0) =1, by Euler's method y(0.5) = dx For the IVP None of these 1.65 1.75

A: Solution of initial value differential equation

Q: Solue d?3e 2 +4x=5in zt using methoel I Vorintion of parameters .

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A: The given integral is ∫lnxdx. The rule for integration by parts is given by ∫udv=uv-∫vdu. We have to…

Q: (b) Given that = 3 in steps of 0.2, given that y = 4 at r = 2. dy = x+Vy. Use Euler's Modified…

A: Given y'=x+yy(2)=4   , y(3)=?       h=0.2  modiefied euler method is yn+1=yn+hfxn+h2 , yn+h2f(xn…

Q: 2 -πx²y. = The volume of a right circular cone of radius ï and height y is given by V 3 dy when x 4…

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Q: The tank is a cylinder of radius 4 m and height 15 m. Assume that the tank is half-filled with water…

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Q: Find the sloution of the given DE dy y-x dx y + x = Yexact - y(0) = 1, h = 0.1 at x = 0.5 ? (find…

A: Introduction: Euler's method is a tool that is used to solve an initial value problem numerically.…

Q: where That the value of differentiable she 9(1) = co, g(2) = 0 žin lu g Cya S, 9'(t)= dt Jals 9(t)…

A: Solution:

Q: 3 Méthod to find the intersection points for y = In r and y = x - 5. 5. Use Newton's Method to…

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Q: 2. Use Runge-Kutta method to solve the IVP dy x +y? y(1) = 2. dx ху Use h=0.2 and approximate y(2).…

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Q: 1 The volume of a right circular cone of radius x and height y is given by V Tx y. Suppose that the…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.