Let I:=∬DydA, where D={(x,y): y≤x≤4, 0≤y≤1}.  The value of I is?

Q: Let f(æ, y) axy + az?y+ y³. (a) div(grad(f)) = (b) Find a so that div(grad(f)) = 0 for all æ, y. %3|…

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Q: Compute the absolute and relative errors in using c to approximate x. x = √2 ; c = 1.414

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Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

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Q: let x~ exp0), find B.C.R to test Ho: O3 against H,: 0 2,if4, ds o.05,

A: Exponential distribution: Here, X1, X2,,…, Xn, are iid (independent and identically distributed)…

Q: 327. F(x, y, z) = zi+ xj+ yk; S is hemisphere z = (a² – x? – y?)/2. -

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Q: derrorsinx,y,zbe0.001.Find relative error when x = y = z = 1.

A: Given,                 U=z4                                                  ...(1)  x=y=z=1, and…

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: (c) Is ergodic (d) Is wide sense stationary

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Q: --Let f(x, y, z) = x²y z +2ye²+7, find Se Əx = ? af =? ду =? axdz

A: f(x,y,z) = x2yz +2yez +7 df/dx = 2xyz  df/dy = x2z + 2ez df/dz = x2y +2yez d2f/dxdz = 2xy

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: Find the uncertainty in U, assuming that X = 10.0 ± 0.5, Y = 5.0 ± 0.1, and a) U = XY² b) U = X² +…

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: aw b- if w = x + 2y + z2, x , y r2 + Ins and z = 2r , find the value of ar .rk)

A: We will solve the following

Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

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Q: Q5.Given that W = f(x.y.z)% x+2y+, find : aw aw in terms of s and r, if and x=, y=r +Ins, =2rr.

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Q: Let D={(x,y,z) : x2+y2+z?s 49, z2 0}. Evaluate z dv.

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Q: Find the measure of QP if Q is the incenter of ΔJKL. Also, Find the measure of ∠QJK if Q is the…

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Q: Let cov(X,Y) = var(X) = and h(y) = }* (4y, 0<y<1 %D %3D 45 45 elsewhere Then the value of var(2X +…

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Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: dav dyt if va (x*+y*+z) Show that d'v

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Q: VXEN, 3yEZ s.t. x + y^2 = x - y O TRUE O FALSE

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Q: Let D={(x,y,2) : x2+y2+z?s 1600, z2 o}. Evaluate - z dv.

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Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: If f(x, y, z) = xy + z?x - 3yx z?, find fxy ?

A: If fx,y,z=xy+z2x-3yx2z2 Find fxy ?

Q: If f(x, y) = (x³ + 4y2)3, find and ax ay af Əx af ду II II

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Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: Given f(z, y) = =* y – z'f, show that fry = fyx-

A: See the attachment

Q: Let x be a c.r.v., the E(x4) can be founded by xf(x) dx. O True False

A: Given problem Given that   Let x be a c.r.v., the E( x4 ) can be bounded by ∫-∞∞xf(x) dx   Ans)…

Q: of ALL explanatory variables x2, x3,

A: There will be various methods to test the significance of the exploratory variables in the…

Q: Disprove: X={r1, 12} iff V, (z E X +x=VI=T2)

A: To do: Disprove the statement…

Q: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: Let f(x, y) = y? – x? and g(x, y) = e²+y. Verify that div(ƒVg) = fV²g+ VƒVg.

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Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Compute the absolute and relative errors in using c to approximate x. x = e; c = 2.718

A: To Determine: Compute the absolute and relative errors in using c to approximate x. Given: x = e; c…

Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: Let f(r, y) = 2ry +3x?y2, then fry

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Q: Use the Midpoint rule to deterine the Intergral for the error Function (erf)(belou) 4caurete to…

A: ∫01e-x2dx here we can take 4 interpolation point so n=4 so h = (1-0)/4 = 0.25 x0=0 x1=0.25 x2=0.5…

Q: Consider f (x, y) = re63ry f-(x, y) = e63ry and fy(x, y) = %3D e63ry

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Q: Let X and Y be chosen uniformly and independently from the interval [0, 1]. (a) Are X > Y and max{X,…

A: Let X and Y be chosen uniformly and independently from the interval [0,1] We choose  a) Are X&gt;Y…

Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: Q4 * If f(z) = z? ;z = x + iy Show me u(x, y) ;v(x, y) Determine ux; Vy|

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Q: If || f(t, y) dA > 0, then f(x, y) > 0 for al D (x, y) in D.

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Q: Suppose that you want to test H,:P-0.55 against H,: P + 0.55. The appropriate criti values are A)…

A: Given hypothesis test whether the population proportion is 0.55 or not.

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.