Let Ean, Ecn, and Ed, be series with THEOREM 10–The Comparison Test nonnegative terms. Suppose that for some integer N dn < an < Cn for all n > N. (a) If Ecn converges, then Ean also converges. (b) If Ed, diverges, then Ea, also diverges.

Q: (6) calculate the inrtantanco us rate of at point (4,1,2) in the change of 9 direction of the vector…

A: This is a question of multivariable calculus, the calculus of several variables.

Q: Suppose the symmetric equations of lines l1 and l2 are = 2 – y = z and x = -1, 2 3 espectively.

A:

Q: (b) Can we differetiate and integrate an infinite series of function? When and how? Examine the…

A: yes we can differentiate and integrate an infinite series of function. Below is representation how…

Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(x,y, z) = 4.x +2y + z subject to r…

A:

Q: 2) Find the o - Congugates ot; c) 5

A: 2. To Find: θ-conjugates of  (c) 54 (d) 1+2

Q: Next question Contruct a glide reecion of angle ABC using vecter vand relection ne

A: We need to shift the figure in the direction of given vector, equal to the length of the vector.…

Q: Let F be a field and let B be an nxn matrix over F. Then B

A:

Q: Calculate the flow in the field F along the path C. F = -5 i + 4 j + 8 k; C is the curve  r(t) = 2…

A:

Q: part e

A: The time after which we encounter the next marker is determined as shown below.

Q: Question #6 C13: "Use derivatives to describe and analyze key features of a graph and sketch…

A:

Q: Rey's father is four times as old as Rey. Five years ago he was seven times as old. How old is each…

A:

Q: A company estimates that a certain piece of machinery will have to be replaced in five years' time…

A: Solution :-

Q: Consider the vector field F = (3x + 5y, 5x + 2y). O The vector field is not conservative The vector…

A:

Q: Match each linear inequality to its appropriate graph. Question -x+y>4 -3x+4y> 12 5x-10ν < 50

A: Solution:-

Q: Solve the following linear equations using the 5 methods: (Gaussian Elimination, Gauss-Jordan…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the volume of the solid that lies between the paraboloid z 2x+2y' and the plane Find the volume…

A:

Q: 1. Find an equation of a curve, such that at each point (x, y) on the curve, the slope equals twice…

A: We have to find equation of curve.

Q: -7 for 0 <x < 4, Let f(x) = - x for 4 < x < 6. Compute the Fourier sine coefficients for f(x). Bn…

A:

Q: dz Suppose z is a function of x and y, and tan vy? + x² = z*e®v. Solve for dz and dy

A: The given function is                                  tan y2+x2=zxe6y

Q: Use the Gauss-Seidel method to solve the following system. Compute the errors. 10 2 -1] [X1] 41 -3…

A: Solution :-

Q: Solve for the given linear inequalities: -3x + 4y > 12 Step 1: Change the inequality sign to an…

A:

Q: Q1: For the given matrix A, find (a) The rank of the matrix A, (b) a basis for the row space (c) a…

A:

Q: Prove thatc "is a vector space over the field of real numbers as well, for any n

A:

Q: Duse the Euler Method method Solve the: Saytanrs tan x-Sinzt, yl0)=1 ,hz0.l 0.1

A:

Q: Let E be the surface with equation (y – 4/2)2 1. | 32 52 42 (a) Give equations of the traces of E in…

A:

Q: Which of the following is a mathematical sentence? the supply y doubled 12 larger than x r…

A: The supply y doubled is not a mathematical sentence 12 larger than x is a mathematical sentence…

Q: 6) The largest interval in which the solution of the initial value problem et (cost)y" +ty 5 %3! t-3…

A: y''+p(t)y'+q(t)y=r(t), given initial value at t0 This equation has unique solution in the interval…

Q: Answer the following using Jacobi Method. Show complete solutions. Answer should have atleast 5…

A: here we consider x1=x, x2=y, x3 =z  So equation become

Q: 5. Determine whether the closed interval [a,b]is homeomorphism to the closed unit…

A: This is a problem from topology.

Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…

Q: Homework Hw4: Find the volume of the wedgelike solid that lies bencath the surface z 16-x - y and…

A:

Q: 1 2 5 -2 - 1 -2 1 1 A= 4 4 V2 = V3 = 6 3 1 6 9 1 3. 3. 3. 2. 4. 2. 2.

A:

Q: 1. How many four digit mumbers can be formed by the une of digits 1,2346 and 7 if one digit is used…

A:

Q: Find the equation of the line that passes through the points: (-3, 3) and (3, -1)

A: The solution is given as

Q: Evaluate the following limit. 7 cos t+ -7 e-t-1 sin 2t -i- 2t lim k 7t 31 7 cos t+ -7 e-t-1 sin 2t…

A:

Q: Consider the problem min a2 – (21 – 2)³ + 3 subject to a2 >1 Which is the value of u*?

A:

Q: Q4) y" + 9y = x Find the general solution

A:

Q: For the convex set C = {(z,9)+ 13 y.0 < 2.0 < y } (a) Which points are vertices of C? (52/9,35/9)…

A:

Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: Let E be the surface with equation (y – 4/2)2 1. | 32 52 42 (a) Give equations of the traces of E in…

A:

Q: 23. Jake had these balances on his credit card for his last billing period. He did not pay the card…

A:

Q: How can the comparison test be valid when (as proved in equation 1) bn <= an?

A:

Q: а. 10х, + 2х, — х, 3D 27 — 3х1 — 5х, + 2х; — —61.5 X1 + x2 + 6хз — — 21.5

A:

Q: 3. Graph the polar equation and find the area of the region. Interior ofr= 6+3 sin 0

A:

Q: Solve for the given linear inequalities -x + y > 4 Step 1: Change the inequality sign to an equal…

A:

Q: Find the volumes of the solids generated by revolving the regions bounded by the grephs of the given…

A:

Q: 3. Let n > 1 be an integer, and let J : Pn → Pn+1 be the indefinite integration transformation on…

A:

Q: Let A be the sphere having diameter with endpoints (1, –9, –2) and (7, –1, 8). (a) Give an equation…

A:

Q: 4 14 -71 C = -10 7 -14 11 has two distinct eigenvalues such that A1 <. The smaller eigenvalue A1 has…

A: Given matrix  C  is ,                                                            C =4   14-70-10…

Q: A company estimates that a certain piece of machinery will have to be replaced in five years' time…

A: Solution :-