Find the average value of F(x,y,z)=x² + y² + z² over the rectangular solic irst octant bounded by the planes x= 1, y = 1, z=2. ▪▪▪

Q: 9. A carnival attraction tests your strength by how far in the air you can drive a weight with a…

A:

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: As per the question we are given a 3d region S defined as the interior of the surfaces : z=x2 ,…

Q: Using Bisection method find the root of cos(x) - xex=0 with a = 0 and b = 1. Show your solution…

A:

Q: [2 + m 3 1. Given A= 1 a. (AB)¹ - A b. |4A-¹ + 2B-¹| a. 2AB-¹ 1 2 -1 -1 4 5+ ml and B = [-1-m 2 91 3…

A:

Q: d²y ) Solve the differential equation +y = dx² y'(0) = 0. sin(x) + cos(x) with y(0) = 1 and

A:

Q: Show all the necessary figures and solutions to each of the following problems. 2. Find the area…

A:

Q: The general solution of y" + y = sec³ x

A: First we will find the complementary solution for which we will find the roots of it's auxiliary…

Q: Particular solution of y" - 4y' + 8y = x³, when x = 0, y = 2, y' = 4

A:

Q: Using the Matrix Inversion Algorithm, find E-1, the inverse of the matrix E below. 0 0 0 5 0 0 10 0…

A:

Q: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: Suppose the rule ²[ƒ(-2,−1)+4ƒ(−2,0) + ƒ(−2,1)+ ƒ (2,−1)+4ƒ (2,0)+ƒ(2,1)] applied to 12 solve f(x,y)…

A: Given: The rule, 23f-2,-1+4f-2,0+f-2,1+f2,-1+4f2,0+f2,1 is applied to solve ∫-11∫-22fx,ydxdy.   To…

Q: Which polar equation is represented by the figure?*

A: Solution :- this graph is  r=a sin(2theta)

Q: II. Find the general solution of the following differential equations. dy x+1 1) = dx 2(y+3) dy 2) =…

A:

Q: Formula valid for matrices? explain why? (A + B)(A - B) = A²B²

A:

Q: If F(x) = ["* e¹² dt, find F(1) and F'(x).

A: If y=f(x), then x is called the input, and y is called the output of the function.  The derivative…

Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x<0xx≥0. If we take x=-2, then f-2=2…

Q: 4- Evaluate the following integral * sin 0 de -5\32 -5√π\32 O 5√n\32 5\32 KIN 0

A: Use Walli's formula to evaluate this integral as in next step.

Q: H.W: Estimate the root of the equation for the following equation usind Newton- Raphson method: 11…

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

Q: On January 1, 2022, Marites deposited P15,000 in a bank that offered 2.5% annual interest compounded…

A: Given that, Amount deposited on January 1, 2022 = 15000 rate (r) = 2.5% compounded monthly, So, n=12…

Q: 5. Given z arctan (;-), Find az/ay

A:

Q: + 8x and y = x² - 4x. e. Find the area bounded by the two curves y = x² - 6x²+

A:

Q: A yacht starts from a harbour and sails for a distance of 11 km in a straight line. The yacht then…

A: Draw and label the diagram depicting this scenario. Use law of cosines to determine the distance.

Q: 8. Let a be the plane that goes through the origin and has normal (1,2,3) and let 3 be the plane…

A:

Q: 10. A certain tank of depth 10 ft is a surface of revolution = formed by rotating y x² about its…

A: Please see the attachment

Q: Find f '(x) and f "(x) at x = 0 using finite difference approximation of O(h²). (Hint: you have to…

A: The table given is as follows: x 0 0.1 0.2 0.3 0.4 fx 1 0.9048 0.8187 0.7408 0.6073 We are…

Q: Find the solution. (D³ + 6D² + 11D + 6)y = 0 -2x Av=ce-tre-te +c -3x By=c₁e*+c₂ C + czte © y =…

A:

Q: Let (X, d₁) and (Y, d₁) be metric spaces. Let f: X Y be continuous function, then f-¹(G) is open in…

A: Solution

Q: c. Is D30 a distributive lattice? Explain. d. Is D30 a Boolean lattice? Explain.

A:

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. In(x+1)³ 3. Lim 3 X→∞0 6x

A:

Q: The terms T₁, T₂, T,,T,,T, of a sequence are given as follows: T₁ = 1=1 T₂ = 3=1+2 T₁=6=1+2+3…

A: The general formula for the sequence is already calculated as Tn=12nn+1. Use this formula to…

Q: Q/६ using integrat test: n - 14 (n+1)(n-4) Test the following series

A:

Q: Simpson's Three-Eighths (Use n = 12) 9. So¹ (3x²+3) dx 10. (2 sin x + 3cos 2x) dx

A: First we find general solutions: 9.  ∫13x2+3dx=∫13(x2+1)dx=13∫1(x2+1)dx=13tan-1x +c    then…

Q: y" − 7y' +6y=−e* [17 cos x-7 sin x] y(0) = 4; y'(0) = 2; -

A:

Q: The Minimum point of y = 8x+4 (x-2)²

A: Use a graphing utility to plot the function. Use the utility to determine the minimum point.

Q: 5. Let a₁ = √5, (a) Find the recursion formula (b) Assuming the sequence converges find its limit…

A:

Q: Let

A:

Q: Consider the constrained optimization problem: min f(x), subject to ||ï||₁ ≤ 1. We apply a projected…

A: Solutions

Q: Q4: A vertical steel plate of dimensions 3cm x 3cmamd negligible thickness is in steady state…

A:

Q: a) Find a closed form of the solution using the method of Taylor series about x = 0. b) Use Euler's…

A:

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We will sketch the region bounded and find boundary curve to use polar co ordinate for volume .

Q: Consider the following optimisation problem min f(x, y) = x + y − x2 subject to x + y ≤ 1 x ≥ 0, y ≥…

A: As per the question we are given a optimization problem as : min(x,y) x+y-x2 s.t. x+y≤1 ; x≥0 ; y≥0…

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 5. Lim xsinx x→ 0+ 5

A:

Q: 1. [4(cos 12° + i sin 12°)]³. 3. [√3 (cos 25° + i sin 25°)].

A:

Q: 1 Consider the series (-1)-¹ Σ(−1²+ (x+1)* where b is a given non-zero constant. Find the nb2n 1=0…

A: Infinite series: An infinite series is represented by ∑n=0∞ anx-cn, where an is the coefficient of…

Q: Given a differential equation as d²y x2 dx² +4y=0. dx By using substitution of x = e' and t = ln…

A:

Q: X 1 4 7 9 11 f(x) 12 -23 -15 33 -13

A: Lagrange's interpolation polynomial for n points can be defined as:…

Q: List all the ordered pairs in the relation R = {(a, b) | a divides b} on the set {1, 2, 3, 4, 5, 6}

A:

Q: dius 9 units and center dius 3 units and center

A:

Q: Find the general solution of D.E. below: (x-2y) dx + (2x+y) dy = 0

A:

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim X→2…

A: