PROPOSITION 3.2. A sequence (an) converges to a if and only if every subsequence of (an) also converges to a.

Q: 69 dx J-9 x2 + 4x + 8 6.

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Q: Eighth grade P.9 Reflections over the x- and y-axes: graph the image 74Z Learn with an example v Gra...

A: When a point is reflected about the coordinate axes or any other line, a new point is produced. The ...

Q: )= x' tan" -1 y X X

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Q: (-1)"n For positive integer n, let a, = 3" (a) Determine whether the sequence {a„} is convergent. (b...

A: Z n

Q: solutions of the above eqation is given by y1(x) = sinh(2x).  The solution of th

A: Introduction: For differential equation y'+p(x)y=q(x), the solution to this differential equation is...

Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). - a...

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Q: m at x=C m at x = 0 m at x = 1 m at x=

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Q: Using the diagram to the right complete the following. How many chords are in this diagram? A A. 4 B...

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Q: 5. Let n be a positive integer and p1,P2,P3, . „Pn be n distinct primes. If m is a positive integer ...

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Q: 16. Solve each of the followir (a) (x- 2)2 0 (c) x2 - 10x – 3 > 0

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit t...

Q: Let T: M,2 → R be a linear transformation for which 1 0 11 5, = 10 %3D 0 0 1 1 1 15, = 20. %3D 1 0 5...

A: let T:M22→ℝ be a linear transformation for which  given  T1000=5 , T1100=10T1110=15 , T1111=20 find ...

Q: 1. Sove for the orthogonal traectories Y- 3X + 1 -3X Ce

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Q: To submit Let S be the set S = {a+ bk :a,b € R}. where k is a formal symbol. Define addition and mul...

A: Given: S=a+bk : a, b∈ℝ addition and multiplication operations on S are defined as, For x, y∈S, x+y=(...

Q: of the eigen vector of a distinct eigen values th vector of matrix A?

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Q: 1. Determine the real roots of the equation: f(x) = -0.5x + 2.5x+4.5: a. Using quadratic equation. b...

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Q: Solve the following function operation. Show complete solution. Let f(x) = 5x +5      g(x) = x+3 ...

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Q: Find the surface area of the figure below. 5 cm 13 cm 5 cm 8 cm 6 cm

A: Here, we have a figure of a triangular prism as it has two triangular bases. We will find the surfac...

Q: Coloring the vertices, find the chromatic number of the following graph G. Select the correct chroma...

A: Chromatic number of the graph

Q: 1. d = 9in VOLIME (INTRIS O F) VOLUME(DEARST TENT)

A: The volume of a sphere is V=43πr3, where r is the radius of the sphere. The radius is half of the di...

Q: Revision worksheet: Analytical geometry C-3) A(4; 5), B(a;b) and C(8;-3) are the vertices of AABC. P...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

Q: The 2nd approximation to the real root of the equation ex – 4x = 0 with initial guess xo = 0.3 using...

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Q: 1. In the ring Z[r], let I = (r* – 8). (a) Let f(r) = 4r³ + 6x* – 2r³ +x² – 8r+3 € Z[r]. Find a poly...

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Q: (ztan 2 +1) dx – x dy = 0

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Q: Problem 7. Let A be an mxn matrix and a be a real number. Show that if aA = 0mxn; then a = 0 or A = ...

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Q: 2y" – y" – 6y' + 5y = 0 |

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Q: Which of the following is equal to 2 ? A 6. 7 13 C 7 17 7 3. 517 B.

A: The mixed fraction: xyz is same as the expression: x+yz.

Q: 2. Consider an unforced spring-mass system whose displacement is modelled by the ODE m x(t)" + cx'(t...

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Q: Determine the truth value of each statement. There exists an integer x such that 2x − 5 = 12.

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Q: Points P, Q and R have coordinates (6, 3, 3), (10, -8, 15) and (18, 15, 22) respectively. (a) Find t...

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Q: Determine the Mc Laurin Series Expansion of the function and express the terms in power series formu...

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Q: . The principle of work and energy. A particle of mass m moves along a curve under the action of a f...

A: This is a problem of Kinetics, Application of differentiation.

Q: y''-3y'+2y=5e^3x,y1=e^x

A: Reduction of order is a very significant and basic method to solve higher order linear differential ...

Q: How many hands of 5 playing cards (from a standard deck) contain exactly one pair of cards of equal ...

A: We have to determine the number of hands of 5 playing cards containing exactly one pair of cards of ...

Q: please send handwritten solution for part a

A: We use rank rules.

Q: Find the range of the quadratic function. y = 3x+12.x+ 13 + 12x+ 13 Write your answer as an inequali...

A: Given: y=3x2+12x+13 To find: Range of given quadratic y=3x2+12x+13.

Q: dy/dx = sec 2xsec³y

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Q: Q1 / Find the root of the equation x= Cos x, using simple iteration method.?

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Q: Find the area of the region bounded by e21.2.png f(x) = = a/4 + 3x – x² and the x -axis using Left R...

A: Left riemann sum  ∫ab  f(x)dx≈Δxf(x0)+f(x1)++f(x2)+....+f(xn-1)+f(xn)

Q: Plot 1 Plot 2 2. y2=xsin(x) 2.

A: To sketch the graph of a function using MATLAB, "plot" command is used. To arrange the figures side ...

Q: The 2nd approximation to the real root of the equation ex – 4x = 0 with initial guess xo = 0.3 using...

A: Given equation is  ex-4x=0 we have to find the 2nd approximation to the real root using Newton-Raphs...

Q: Solve the system of linear equations using Gaussian Elimination method. x + y - z = -2 2x - y + z ...

A: we have given the linear system of equation x+y-z=-22x-y+z=5-x+2y+2z=1 we have to solve the linear e...

Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m) + (-n) = - (m + n)

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Q: Find the derivatives of y with respect to x: a) y = xe* - e* b) y = e(1x+) %D c) y = e*(sin x + cos ...

A: (a) The product rule of differentiation is as follows: uv'=u'v+v'u The required differentiation form...

Q: Find the solution of y'' (x) = y(x) that fits in origo and goes through the point (ln2,(3/2) )

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Q: Example: Evaluate J = e-x dx by using trapezoidal rule, n=10.

A: Given J=∫01e-x2dx and n=10

Q: etiva method

A: given f(x)=x3-x-1 in the interval [1,2] f(1)=x3-x-1=1-1-1=-1 f(2)=x3-x-1=8-2-1=5 f(1)f(2)<0  ther...

Q: Let E be the set of all positive even integers. Prove that E is countably infinite by defining a map...

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Q: e Product Rule to differentiate the function    y=e−11xsin(10x)y=e−11xsin⁡(10x)           Fill in ...

A: In the given question, the concept of derivatives is applied. Derivative We can use a derivative to ...

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: We will first try to write the given series in simplified form then we will check whether given seri...

Q: 1. Express 2/3 + 2i in polar form.

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