1) Find a formela for the fucki rmula tier y=f(x) whose amaph consists of thre nents as in the fllowing figure y=fix) 4 1 7 14

Q: 1. A natural cubic spline S.on [0,2] is defined by (S.(x) S(x) = {x)=1+ 2x-x s,(x) = a+ b(x- 1) +…

A: The cubic spline is defined as: Sx=S0x=1+2x-x3 if 0≤x≤1S1x=a+bx-1+cx-12+dx-13 if 1≤x≤2 From…

Q: B If f(x) has a local minimum at ra, then which of the following must be true? O f'(a) > 0, f"(a) 0…

A: We have to find the correct option.

Q: Find the value of c > 0 such that the regionbounded by the cubic y = x(x - c)2 and the x-axis on…

A:

Q: • Suppose that the mass in a mass-spring-dashpot system with m = 25, c = 10, and k = 226 is set in…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 3) Let PIASR ond Thi AxC ßeD. Then his a Anction. Te Ø # 4 B and ø 7b cD then that h'(Y x Y% ]=…

A:

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

A:

Q: Q10. Juppoe fG)= 25-t2 5+ Cos 10 For yehat nlece ()f a does fa) Laue a local minimum.

A:

Q: 0. gy c ube a losed Cont Conlainig he okigin it. Pycoue thal az 2.

A: I have used Cauchy integral formula

Q: 10. Suppose that a point (X, Y) is chosen at random from the circle S defined as follows: s= (x.…

A:

Q: 5 Considor the inter ral I= i) Estimate I using n=4 trapezids. = -3 2) Estimste I using Simpson's…

A:

Q: Take simplifying voxel Ax= Ay= L length of the diagonal = 1. For the projection (e.g. in any…

A: In 3D special effects, a voxel represents a worth on an everyday grid in three-dimensional space.…

Q: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

A:

Q: (2) Find a smooth curve a in GL(2, R) passing through the identity such that a'(0) 1 0 Justify your…

A:

Q: (f) One of the following 2nd order linear PDEs is elliptic: (A) + 2lay theo (C) 1-2y + ly <<=0 (B) -…

A:

Q: AXYZ is isosceles with base YZ and M is any point on YZ. Prove that a. ZXMY > ZY Z. b. XM < XY M

A:

Q: Consider the following semilinear first-order PDE ди ди +y ду = xe (i) Find the general solution to…

A:

Q: Osing lagoange's me thad, find the marimum co minimum 4 =x°ty'4 z* subjeit to the condition ax° tby?…

A:

Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

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

Q: 3. Show that the equation for G(r,ø) can be separated by choosing G(r,ø) = R(r)P(ø) into OR Rar ar 1…

A: Introduction: The Laplace equation is one of the most important partial differential equations. It…

Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

A:

Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: Find the value of c such that the regionbounded by y = c sin x and the x-axis on the interval [0, ∏]…

A: Given y = csinx and the region bounded by y = c sin x and the x-axis on the interval [0, π] has area…

Q: 2 let C be an arbiterery curve from l0,0) to D). (2,4) Evala vute: (3x² oy, x-2)- dio

A: To find the value of the given line integral.

Q: 2. A firm produces two goods in pure ompetition &amp; has the pllowing TR &amp; TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

A:

Q: Lose Tayor's theorem to obeah amepper band fer the enrar of the Mthrs approximation gNen a…

A: Given data: c=0 sin0.5≈0.5-0.533!+0.555! Using Maclaurin series expansion: sinx=∑n=0∞-1n2n+1!x2n+1…

Q: 3. Compute x In x da both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

A:

Q: 7. let E be the reyion bounded by curve 2+2 in the yex? fint quadant let u xy, Vzy-x d Czry)…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Mathematical modeling is the real-life application of the differential equation. One such important…

Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: 3.5 Given that H = x'a, + ya,, evaluate H· dl, where L is along the curve y = x from %3D (0, 0) to…

A:

Q: ) ind the standard matux Der the stated in Re 2Anylection about the linn yez Golleued ya 60°c.…

A: We'll answer the first question since the exact one wasn't  specified. Please submit a new question…

Q: 7. Evaluate f F dr, where F(x, y, z) = xyi+yzj+zxk and C is the arc of the twisted cubic given by x…

A:

Q: Q.1: lel I 1,2,3]. Ts Prove that Tz and T3 Gre topologi es for X Ta is topolagy far y Ti is nat G…

A:

Q: Lee 3.1. A Usc the same at XS07=( X4 Tagler polynnencal polynimial at C=0. Dsing the algebraz…

A: To find the Taylor's polynomial of a function f(x) at , the remainder and the error, use the…

Q: - Emluste ihe given limt ké", ut, 177 2. Compute 1he dovivadv'e A she given vactor hu. F()-…

A: Since you have posted 3 questions here, i can answer only first one. Please reupload remaining…

Q: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: 13. Point P is the centroid for AMNO. Calculate OQ if ON = 17. Round to the nearest tenth if…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Water is leaking from a circular hole(in the bottom) whose area is Ah. When water leaks…

Q: 3. Given the closed curve defined by y = vx in the first quarter up to 1000 = x (area production),…

A: FIND: a) how many unit squares it contains b) number of squares needed in the cover

Q: (4) In the figure, Y is compact, BEX*Y. Show that T,(B)s TB) clesed X (T, is the nýuchikn funebran)…

A: Given that Y is compact and B⊂closedX×Y. The objective is to show that, π1B⊂closedX Let's define,…

Q: Sketch the reglon enclosed by the gven curves. Dedde whether to Integrate with respect to ror y.…

A: Area between two curves

Q: Create a unique aNadratic furncbion in vertex form Ehat mects the following criteria: - hos an aris…

A: Given: For quadratic equation  the axis of symmetry x=-5 minimum of y=-9 wider than the quadratic…

Q: QUESTION 1 Compute [[ ev** where Q is bounded by y = V100-x-z AP 2++ and y = 0.

A:

Q: 3)if f(2)=1/z, has zero of order mat z=0, then f(z) has a zero of order m at d) e a) ∞⁰ b) 0 c) 2in²

A:

Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: 17. Let AXYZ be circumscribed on O R, and let XS = 5, SY = 32, and YZ = 64.* *Image not set to…

A:

Q: 19.22. Find the value of the integral Sc[(z + 2)/2] dz, where C is: (a) the semicircle z = 2e", for…

A:

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.