+oo 1 Σ -1-n n=1 WI

Q: Is the series convergent or divergent? Explain in minimum of two sentences. +oo Σ n2 – 1 Un n=1 n2 +...

A: we have to check the given series is convergent or divergent.

Q: Suppose that the function g is defined as follows. 2 if -3.5 <x<-2.5 -1 if -2.5 <x<-1.5 g(x) = if -1...

A: Red line denote the graph of function  draw that whatever given in question its like a greatest inte...

Q: 5. Write the formal proof that 2"+2 + 32n+1 is divisible by 7 for all positive integers.

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary functions....

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Q: y" - 6y' - 7y = e' sint Find Particular solution cnly

A: Note. : - According to guidelines here solution of only firt question .

Q: Let F : R" → R™ and g : R" → R. Prove that d(gF)[a; h] = g(a)dF[a; h] + F(a)dg[a; h].

A: let the functions be  F:ℝn→ℝm , g:ℝn→ℝ prove that  dgFa;h=gadF[a;h]+F(a)dg[a;h]

Q: 3. A rectangular prism with dimensions 6 m x 4 m x 8 m (l x w x h) is shrinking. 8 m 4 m 6 m Answer ...

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Q: Market research for a certain ice cream company indicates that if the price per cup of ice cream is ...

A: solving first 3 sub parts: demand=x price=p

Q: Date.... x x) pO od { (x) = x 37

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Q: dy _ 4 y – 3x dx 2x- у | !!

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Q: The equation of the hyperbola that has a center at (4, 6), a focus at (9, 6), and a vertex at (0, 6)...

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Q: Problem 2. Solve the following LP problem using the Simplex Method. Use the smallest- subscript rule...

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Q: 2x3+2x² – 95x+40 -dx x3+x2 – 20x Evaluate Then, write the coefficient of the integral: Blank 1X + Bl...

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Q: Q1:- Solve the following DEs:- dy + 2x³y = y³x³ dx

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Q: 3. A rectangular prism with dimensions 6 m x 4 m x 8 m ( x w x h) is shrinking. 8 m 4 m 6 m Answer t...

A: Note: We know that the volume of a rectangular prism is = length x width x height. Also the volume i...

Q: Suppose you are taking a bus trip from your home in Florida to California. There are seven different...

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Q: Let a be a real number. Consider the series an Σ cos(n7); An, where An = 2n + 1 n=0 (a) Is it possib...

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Q: l2: = 1-s, y = 3+ s, z= 3+2s l: =1+t, y = 2- 2t, z= -3+t Determine whether the given lines are paral...

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Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: f(x) = x^3 - 9x^2 - 45x - 27. Find the remaining zeros given that -3 is a zero of f(x). O (-3, -6 + ...

A: Given f(x) = x3 - 9x2 - 45x - 27

Q: - 48x3 – 80x2 – 70x – 126 dx Integrate: 16x2 + 25 + C

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Q: a. Consider the system of differential equations given by: -3 34 y, Y1(0) y = -1 where some initial ...

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Q: f (x) = 5e0.5x at X = 2, find the relative approximate error using value 1. Given from h = 0.25 and ...

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Q: O Lulion laflace Luma fanm of LiS Con t dt G(4) = If L[fla)] = F(S) thin L[ fl4] = (1," " a (tive in...

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Q: Question 1. Consider the sequence : 5,9,13,17,21,.. with ao= 5 a) Write a recurrence relation for th...

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts fo...

Q: Solve, using Pascal's Triangle (x – 4)5

A: Pascal's triangle 

Q: Consider the following LU decomposition of the given matrix: 1 -1 4 5 -3 6 0 0 oT2 1 -1 2 0 a22 U23 ...

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Q: Consider the series (In(2n + 1) –- In(2n - 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,} ...

A: We first check whether the given sequence in (a) is convergent or divergent.If it is not convergent ...

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

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Q: f(x)=6x-10 , g(x)= x^2+3x+8 (gof)(-2) = %3D 55 none of these 25

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Q: Let P(x)=-x3+2x1²-6x²-5x+-1 and D(x)=x+1 Determine the remainder when P(x) is divided by D(x)

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Q: roblem 4. Let w, y, z E Z[i] such that wyz, and let d be a gcd of w and z, show that wyd.

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Q: Formulate one given 3x3 equation (3 equations and 3 unknowns) and one given 4x4 equation (4 equation...

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Q: Problem 3. (a) Determine the cosine of the angles of the triangle whose vertices are A(1, –2, 1), B(...

A: The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square...

Q: cosQ -sinQ Rotation matrix on the plane (2n - 2). R = sinQ cosQ : : -W RWR' = w W = show me that the...

A: Given R is rotation matrix such  that R=cosQ-sinQsinQcosQ also there is matrix  w^=0-ww0 we have to ...

Q: CONVERGENCE TESTS AND MACLAURIN POYNOMIAL 6. a) Make a conjecture about the convergence of the serie...

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Q: 6. (a) Suppose U, W are subspaces of V. Show that (U + W)° = U°nW°. (b) Suppose V is finite-dimensio...

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Q: Ollivanders is a wand shop for wizards in Hogwarts. It has been estimated that when x wands are prod...

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Q: 16y" + 8y' + y = x +6 3.

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Q: 2. a. Fill in the table and sketch the graph of the following equation. f(x) : -2x - 5 3x + 18 Verti...

A: Given: 2. a) f(x)=-2x-53x+18 To find: Vertical asymptote, horizontal asymptote, x-intercept, y-inter...

Q: a) Draw an accurate graph of the portion of f(x,y) that is above the xy – plane. b) Describe the 2D ...

A: We have to graph the function.

Q: nethod; Inz Vina)-y²

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Q: х+2 у-1) dx- (2х+4 у-3) dy%3D0

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Q: dy -3+5 y dt

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Q: sin (2?- 4a) lim, 4 sin (x2 – 10x + 24) -10x +24)

A: LHospitals rule indeterminate form.

Q: Use the definition of the functional limit to prove the following: (a) lim 4x + 3 = -5. x→-2 (b) lim...

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Q: Is the series convergent or divergent? Explain in minimum of two sentences. +oo Σ n2 – 1 Un | n=1 n2...

A: The main objective is to test the given series is convergent or divergent.  We can examine the conve...

Q: Jan deposited an amount of money in the bank. If interest rate of the bank decreases from 4 3/43% to...

A: The rate of interests can be simplified as follows: 4343%=17543%,412%=92%

Q: 6. Find the 6th term in this arithmetic sequence {13,26,39, ...} 7. Find the 5th term in this geomet...

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Q: 200 1. The function: P(x) = 2x + 0 <x < 0, models the perimeter of a rectangle of dimensions x by 10...

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