1, fund warginal cictribution for h(x) for 2. Fud condhtimal pdf4 t) . Estaati yi/ a) V. Estuate E(/x=0) こク

Q: 3. Variation of Parameters у" — 2y' + у |

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Q: cot (특) sec () 11. 12. 6.

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Q: 4.) Evaluate: xe* dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: Find the Be2uation os the tangent line to thegnaph of f0= at 7) 7. The equation os the tangent line…

A: Tangent is a line to the curve that just touches the curve at a point.

Q: c) lime**sin.x =

A: Limx-infinity sinx

Q: Find if y = tan- 5). Select one: A. 1-) В. 1+ (1 – 2)* C.d - 2 O D. I+ (1 - 1)* OE.+ (1-)

A: Given function is We know that derivative of tan inverse x is 1/1+x^2,so

Q: @ check ahether the Pellowing is Pdf Rx) = %3D x2-3(x-1)2 1<2く2 32<x<3

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Q: derivatma ofy= ff) -glglw)

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Q: sec Vn du in

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Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Ql Find se dx |

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Q: 6. J de cote sin²0

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Q: 5)find y y= Inl-decx +tanx)

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Q: | cot* xcsc' xdx x csc"

A: Let the given integral be y -y = ∫cot4xcsc4xdxy = ∫cot4xcsc2xcsc2xdxy = ∫cot4x1+cot2xcsc2xdx…

Q: sinty

A: This is a basic integration problem

Q: Sece. tano do seco Jsec'o -1 Seco . tanodo feco· Jtario feco. tono do Seco . tomo

A: we have to solve integration.

Q: The expression of Absorption's law is given by what?

A: The expression of Absorption's law is

Q: Differentiate, hcx) = In (x-Vr

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Q: tan' sec? 그dr 26. 28. 7 dr - 10

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Q: Entae akale VX+39 dx

A: We have to solve

Q: (X-5) + form Get it into y= and enter it into your Cal culator. Use the tables to show your Ver…

A: Given, x-529+y+624=1 This is the equation of Ellipse. Now…

Q: tan³ r sec' rdr

A: The given integral is ∫0π4tan3x sec4x dx. Let u=sec x. Then du=sec x tan x. Then, the lower limit…

Q: Ex) Consider flx)=x^2", x= 1.7,2.0, 2.3,2.6,2.9 P foruard diff. central diff Backuard difp. find…

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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.