Σ () n+1 \ 3n 4n n=1 converges diverges

Q: y = -x^2 + 4x , y = x^2 - 6x + 5 , x = 0,x=1 O 2.012 sq. units O 2.022 sq. units O 2.032 sq. units O...

A: The given problem is to sketch the given graphs and intersection points and also find the area forme...

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Q: 22n+1 Σ 52n+2 n=0 4 25 8 525 2 21 diverges Drevious Dage Next Page || 2/15

A: To find Whether the series converges or diverges. 

Q: Let k be a positive integer. Use induction to prove that (k −1)n+1 + k2n−1 is divisible by k2 −k +1 ...

A: To prove that k-1n+1+k2n-1 is divisible by k2−k+1 for every positive integer n using Prinicpal of ma...

Q: Q2. Find the radius of convergence and interval of convergence of n! n=02"

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Q: 11. The number of cellular phones in use in the United States is increasing exponentially. The numbe...

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Q: E (e+1)" converges for 3" n=0 None of these O-4 < x < 2 O-4 < x < 2 O-4 < x < 2 O x < 2

A: To find  The interval of convergence. 

Q: Let x1 = 1 and xn+1 1 for n e N. Show that this sequence is convergent and find its In + 2 limit.

A: I have shown the sequence is bounded above and monotone increasing which implies sequence is converg...

Q: e induction to prove that

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Q: 7 2 3 4 Which is A-1 a) -3 2 4 b) -4 2 3 c) ( 2 -1)

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A: Evaluation of the double Integrals  

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A: Summation evaluation

Q: Use the Geometric Series Test to show that 0.3+0.03+0.003+…… converges.

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Q: Solve the following: (Show all details) 1. Let matrices be [3 0 4] A = |-1 2 2 5 4] [o 2] C = 2 4 li...

A: It is given that ; A = 304-122654  ,    B = 0-5-3-524-340  ,     C = 022413  ,  D = 61-47-83 u = 20-...

Q: 3. Let E be the set of rational numbers in the interval (0, 1). Let XE be the characteristic functio...

A: Here given characteristic function as χEx=1x is rational0x is irrationalwhere x∈0, 1 Clearly χEx is ...

Q: Let {u1, u2, u3, u4} be a linearly independent set of vectors. Select the best statement. OA. {u1, u...

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Q: Prove that for all integers n > 2, f(x) = x/n is continuous on [0, 0).

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Q: f(t) = 2Ct -4)

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Q: Characteristic Equations Q1.Find the general solution of following PDE equation (a) (5x + R)uz + (7x...

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Q: A periodic function of period 2n is defined for 0 1) u÷- x- 2π ( 5π< x < 2π) Sketch f (x)for (-27 <...

A: Given: Let us consider the given  function, fx=x0≤x≤12π12π12π&lt;x≤π-12ππ&lt;x≤32πx-2π32π≤x≤2π

Q: 6 1 2 A = 3 4 The determinant of A is -1/2 O 2 O 1/2 -2

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Q: - 75ec 3x+tan 3x(sec 3x+tan 3x) cos 3x dx (7sec 3x+tan 3x)In 7 + C 7secax+tan ax + C 7 In 3 3 O c B ...

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round yo...

A: Given:   The line given by the set of parametric equations. (3, -8, 4); x = 2t, y = t - 3, z = 2t + ...

Q: A number-theoretic function f is said to be multiplicative if f(m, n) = f(m)f(n): %3D :Select one Fo...

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Q: 1 Set up and evaluate , 6x dA, where R is the rectangular region with corners (-2, 0), (3,0), (-2, 2...

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Q: Consider the variable coefficient linear second order non-homogeneous ODE x?y" – 2xy + (² + 2)y = 3x...

A: First we calculate complementary function yc(x) and then calculate yp(x) using variation of paramete...

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula. ...

A: Solution:   This is an equivalence relation since:A U Y = A U YA U Y = B U Y implies that B U Y = A ...

Q: 3. Find the area of the surface having parameterisation r(u, v) = (uv, 3uv, v), where u E [-2, 2] an...

A: Surface area of the surface

Q: x²y" +xy' – 4y = 2x*

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Q: ди One-dimensional heat equation at dx

A: To solve the equation we can use method of separation of symbols. In this method we put our dependen...

Q: 8. Solve the differential equation (x+y) = a². dx dy Solve the differential equation tan (y- x)= 1. ...

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Q: 1 2 A = 3 4 What isA?? a) 7 10 (1s 22) b) 1 4 16, c) impossible to calculate

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Q: From the following statements, choose the one(s) that are true. OA. The function f(x) = 1 can be rep...

A: Series and sequence, convergent, divergent and radius of converges

Q: S-4 2) F(5) = In

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Q: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².

A: Here we compare r as its basic equation to prove this.

Q: (e– 1)y' = 2 + cos.x -

A: Let us consider the differential equation of the form dydx=f(x)g(y) Rewrite the equation as 1g(y)dy...

Q: Consider the variable coefficient linear second order non-homogeneous ODE a?y" – 2xy + (x² +2)y 3x3 ...

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for you...

Q: II. Prove the following are valid (theorems) using resolution: (You must negate!) 1) (~Q->~P)--> ( (...

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Q: Find a power series for the function, centered at c. 1 h(x) c = 0 8x' %3D Σ h(x) : %3D n = 0 Determi...

A: It is given that fx=11-8x. We have to find the power series representation of the form ∑ an of the g...

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}....

A: Given relation is R = {(a, b) : a ≤ b3}

Q: vitomin B w te n pe e Solution : O let x Ounce of food P. y = Ounces of food Q. This is decision var...

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Q: 3. Compute a basis for the column space, row space and nullspace of the following matrix. 1 -10 -1 -...

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Q: 3. Given an equation of a circle, determine how to find a point on the circle. Determine how to find...

A: Suppose (x-a)2 +(y-b)2 =r2  be an equation of circle with centre at (a,b) and radius is r. Two ways:...

Q: What is the absolute minimum for the function f(x, y) = 4x2 + y? subject to the constraint equation ...

A: For the solution of the problem follow the next steps.

Q: 4. Determine one real root of 8 (sin x) e¯* – 1 = 0 with xo = 0.30 using Newton-Raphson Method until...

A: Determine one real root of 8(sinx)e-x-1 =0 with x0=0.30 using Newton-Raphson Method .

Q: "Let h(x, y) = x² + 3.xy- 6y. What is the amount of the greatest increase of h at the point (3,2)? I...

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Q: 10. (a) Produce the linear Taylor polynomials to f(x) = In (x) on 1 < x < 2, expanding about x, = }....

A: (a) produce the linear taylor polynomial  fx=lnx on 1≤x≤2 expanding about x0=32.

Q: .A man borrows Rs 8160 from a finance company and has to return it in two equal annual instalments. ...

A: Installment = [P x R x (1+R)N]/[(1+R)N-1] where P stands for the loan amount or principal, R is the ...