EX. Apply 4th order Runge - Kutto to s olve the toll Valu e Problem 4'= 44 for hzoid , y(1) =1. and 1s x42

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: . Fing the coefficient of x' and x' 9 10 expanston of any x in the (22- * Find the qe from of (2+ -5…

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Q: Lec 7.1. Evaluate SJ*FI'dx and ard nuerber x +i dx -4.48535

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Q: 1. State the domain and range of {(x, y)|y = + 3}.

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Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: 1.3 Evaluate ſ, Vx dx taking h = 0.05 by trapezoidal rule.

A: evaluate ∫11.3x dx taking h=0.05 by trapezoidal rule according to trapezoidal rule ∫11.3x dx≈Tn…

Q: 3. J2sec (w) - 8csc(w)cot(w) dw from w = л/6 to w = π/3

A: Please see the below picture for detailed solution.

Q: 18.8. (a). Let y be the contour z = ete, - T<0< T traversed in the positive direction. Show that,…

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Q: The power P (in W) in an electric circuit is the product of the voltage V and the current I (in A).…

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Q: 3. y 4 7 D = R = Function?

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Q: 29. Find equations for the lines that are tangent and normal to the curve y = V2 cos x at the point…

A: y=2cosx ,   π4, 1 Differentiating with respect to x, we get dydx=2-sinx=-2sinx Now slope of the…

Q: . Find an equation for the tangent to the curve x sin 2y = y cos 2x at the point (T/4, 7/2). %3D

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Q: Q4) find at t= from the following functions, x= cost. y= 1+sint

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Q: Find y". 6. 7. y =x' +6x y'"3= %3D

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Q: Problem #5: Consider the differential equation (6x + 2xy) = 5x + 6x + 21¹ Problem #5(a): Problem =…

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Q: Suppose that a particle moves along a straight line with velocity - cos(t/2), sin(t/3), te [0, T], t…

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Q: Suppose V - Geom(p) with p = 0.16 and that W = 2V. Find P(W > 8), giving your answer correct to two…

A: Solution .

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

A: Given,          The length of the curve y=lncosx from x=0 to x=π4 .We know that,          The length…

Q: If (Mesin(2x) dx = eSin(2x) + C, then the M is equal to-

A: We will differentiate both sides w.r.t 'x'

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.