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Q: Approximate the sum of the series correct to within 0.00001. (-1)" n° 9 n = 1

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Q: By applying Rolle's theorem, check whether it is possible that the function roots. Answer: ?

A: The given equation is f(x)=x9+x-6 f'(x)=09x8+1=09x8=-1 If f(x) has two real roots then By Rolle's th...

Q: n 3. Suppose G is a group with order 99. Prove that G must have an element of order 3.

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Q: Evaluate: 2sin(3i)cos(3i)

A: Given  2sin(3i)cos(3i) To solve we use following properties: 2sin(θ)cos(θ) = sin(2θ) sin(iθ) = isin...

Q: Let I'(V, E) be a graph. For v E V and e E E, prove the following statements: 1-O(T – {v}) = O(r) – ...

A: Given that ΓV,E is a graph. Let v∈V and e∈E. We know that the order of a graph is equal to the numbe...

Q: Q1; Vsing the Power serieg expansion for cose

A: Power series exaption for cosx

Q: Choose the correct ordered pair that makes the inequality true. 1. x + 2y ≥ 8                     ...

A: Given  x+2y ≥8 . Now  4+2×2=8 , therefore (4,2) is correct order pair. -2 + 2×5 =8 , therefore (-2,5...

Q: Consider the function f : [–1,2] → R defined by f(æ) = x² – 1. On the interval [-1,0] the maximum va...

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Q: whose

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Q: dy Find dx * of y* = sin(e) + xtan-1x. %3D

A: We have to find dydx

Q: Question 2 Use the Alternating Series Estimation Theorem to find the minimum number of terms of the ...

A: We have to find the number of minimum terms of alternative Series.

Q: ,,E R, nxn mathix, Such that For nZ 2 and any X,,X2, if P dis an nxn mattx such thet P dis (P);; =x5...

A: We have to prove the given statement by induction.

Q: If n 2 1, then the Fermat number Fn 22" +1 is prime if and only if %3D 3(F.-1)/2 = -1 mod (Fn).

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Q: iBin a normed space X, the a bsolute convergence ofevery series al ways Implies convergence of the s...

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Q: Evaluate the area under the parametric curve given by x = 2, y = 4t – 2 and above the x-axis on the ...

A: Area of the parametric curves along x+axis  

Q: Find F(s) for f(t) = sin? 4t

A: Solution

Q: -aIa+Ga)Iy -tja) Is =0 --- ーユ2 + Iイ=o eq'n I eqin 2 -2Iz+ Is t Iq t I5 =o--- eg'n s J,-212 = 6 I,- I...

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Q: Find the sum of the convergent series. 1 1 (a) 2n 3n (b) (sin 1)" n=1 9. (c) 8+6+ 27 +... 8 1 ( d) Σ...

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Q: Solve: dy/dx = 2 + sqrt(y - x+ 3). %3D

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Q: 5. Find the maximum and minimum values of f (X, Y)=e 12Y) and all points (x,7) at which they OCcur o...

A: We have to find the maximum and minimum value of f(x,y) in region D.

Q: Solve for a root/roots of the functions x² – 3 sin x + 2 In(x + 1) = 3.5 Applying the following meth...

A: Newton Raphson Method:-

Q: Evaluate L{e" (r +r* –-1)}. 6. A. (s–2)* (s-2) (s -2) 6. 21 B. (s+2)* (s+2)' (s+ 2)* 2 C. (s-2)' (s-...

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Q: Evaluate L{3e cos 10r cos 41. S+1 s+1 A. 2 (s+1) +16 (s+1) +100 S-1 S-1 B. 2 (s-1) +16 (s – 1) + 100...

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Q: Question 2. Consider the function f(x, y, z) = xye-(a+y´+z²), Find all points (a, y, z) such that Vf...

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Q: Find the volume of the solid enclosed by the paraboloids z = 1 (x2 + y²) and z 32 – 1 (x2 + y²).

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Q: must include the entries augmented to the original one. 9. The difference between a complex number z...

A: We have to check whether given statement is true or false.

Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral L{f{t)} ...

A: Given function is f(t) = cos(t),0 ≤ t &lt; π0,t ≥ π

Q: 1 3 -1 5 9. Let A = -1 0 -2 -2 1 1 1 3 (a) Find a basis for the row space of A. (b) Find a basis for...

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Q: Let g(x) bound on |g(x) - T2(x)|, where T2(x) is the second degree Taylor polynomial, centred at x =...

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Q: Use the substitution t= tan to show that secx+ tanx = tan (4+3). %3D

A: We have to prove using substitution t=tan(x/2).

Q: 1- find m n x., min. and saddle points for the following functions : * f = 4x - 6 xy +5y" -20x +26y ...

A: We shall find the maximum, minimum, saddle points for the given functions Consider f=4x2-6xy+5y2-20x...

Q: Approximate the sum of the series correct to within 0.00001 (-1)" n = 1

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Q: 4. Solve this fourth-order ODE by using the method of undetermined coefficients: y" – y" = x. (Sto

A: Introduction: The order of a differential equation depends on the highest order of differentiation. ...

Q: Evaluate the definite integral using the first four Newton-Cotes quadrature formulas. а. x2 cos xdx ...

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Q: Consider the following. u = 3i - j - k, v = -i + 5j + 7k (a) Find the projection of u onto v. (b) Fi...

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Q: 9+5k Consider the series (2+k²)²" k=1 a) Enter a p-series that can be used to determine the converge...

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Q: y In 2 y = In(x + 1) x -In 2 x = -1 In the diagram the region bounded by the curve y = In(x+1) and t...

A: Solution is below.

Q: 1. Determine the FOURIER COSINE SERIES of the following STEP FUNCTION: (-1,0 < x < 2 f(x) = } 0,2 < ...

A: We have to find the Fourier cosine series of the given function.

Q: The mode of a certain frequency curve y = ƒf (x) is very near to x = 9 and the value of the frequenc...

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Q: Given: 2 -2| A = |-1 1 1 1 1 1 B =| 2 1 -1 1 2 1 |-1 1 2 Find the following and show how you get you...

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Q: (2) Let - {b ] E [2 3] A- Is A linearly independent? Justify your answer.

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Q: (b) Let X = (a, b]. Construct a continuous function f : X → R (set of real numbers) which is unbound...

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Q: Five years ago, a trust fund amounting to P500,000.00 was invested at 15% compounded semi-annually. ...

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next ...

Q: y"(x)+ Ay(x) = 0, y(1) = 0, y'(2) = 0.

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Q: Find the average value of f(x,y)= 4x+2y on the region bounded by x=0,y=0, and x + y= 3

A: Introduction: Like a single variable function, the average value of a two variable function can also...

Q: Evaluate f(15) and f(35), given the following data. 10 20 30 40 50 y 46 66 81 93 101

A: The given problem is to find the functional values at given points f(15) and f(35) from the given da...

Q: 1. Given the following complex numbers: z1 = 2 – j, z2 = -3+ j4, z3 = -5 – j6, z4 = 2 + j3 Determine...

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Q: coth x is equal to O e+e* e-e O e-e e+e* a. e +e e-e* e-e e+e

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Q: Suppose you have a function z = f (x, y) defined on every point (x, y). Choose a correct statement a...

A: Correct option is (A) i.e. It is perpendicular to the level curve through the point.

Q: Find the solution of the equationln(x + 2) – e¯* = 0. Using secant method with = 0 and x, = 0.5 Xo %...

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to approxi...