4. Define the followings:            i) Forward and backward difference operator            ii) Numerical differentiation and numerical integration            iii) Numerical interpolation.

Q: Let R be an equivalence relation on A = {0, 1, 5, 6, 8, 9} and R = {(6, 1), (1,6), (6,6), (1, 1), (0...

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Q: (cos20+ jsin20)-3(cos50+jsin50)? (cis40) (5e/20)3 Simplify O a. 125(cos1460+ jsin140) O b. 25(cos140...

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Q: The Archimedean Property says that the set of real numbers have no upper bound. True or False

A: Given a statement , we have to check whether it is true or not.

Q: 8. S 4 csc² 4x dx

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Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n n3 + n2 +1 n=1 converges or diverges...

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Q: . Calculate the volume of the sol Renclosed bư

A: Given, the plane                     4x+2y-z=0 and above the finite region R enclosed by the curves ...

Q: 8. S4 csc2 4x dx

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Q: Using elementary operation, find the lower triangular matrix of Matrix L.

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Q: 3. (a) Show that the Fourier series for f(x) = x², –n < x < n, is cos(nx) 4(-1)"-1 n2 n=1

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Q: Which of the following sets are closed under scalar multiplication? (i) The set of all matrices in M...

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Q: Let f(x, y, z) = In (x² + y + z²). The level surface f(x, y, z) = In 4 is a: Elliptical cone around ...

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Q: Let A E R"X". Use the SVD of A to write down an explicit eigendecomposition of AT H =

A: Given A∈ℝn×n. The given matrix is H=OATAO. Let A=UΣVT be singular value decomposition of matrix A. L...

Q: Sketch the level curve of the function y? f(z, y) : %3D 4 36 for c = 1.

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Q: d. x = 4 and (s + 1) x + y = 3 38 The value of s:

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Q: Which of the following gives a bound for the absolute error centred at a =1 to approximate v2 (i.e. ...

A: Given that f(x)=x Taylor polynomial of degree 2 centered at a=1 for any function f(x) is f1+x-1f'1+1...

Q: Senes anverges diverger. if Aavergent, tnd Hhe sum 2n n t2 to h? + 2n

A: a) ∑n=1+∞2nn+2 here an=2nn+2 using series divergence test if limn→∞an is either does not exist or ex...

Q: Solve by Chain Rule f(y) = / 2y + (3y + 4y2)3

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Q: Given the curve α:(0, 1) → R3 α(t) = (t^2, 2t, (32/9)^(1/2) t^(3/2))  b) Calculate the velocity and ...

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Q: There are three stores. In the first week store I sold 88 loaves of bread, 48 quarts of milk, 16 jar...

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Q: One ladder is leaning against a wall so that its base is 4 ft from the wall and it reached a height ...

A: A triangle is a plane figure with three angles and three sides. If three sides of a triangle are pro...

Q: Solve the following systems of linear equations using Gauss Elimination Method. Use fractions for no...

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Q: Using the Cylindrical Shells Method, find the volume of a sphere of radius 5 cm with a cylindrical h...

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Q: Example 6. Find the Fourier transform of f (x) defined by 1, |x| a and hence evaluate f(x) sin s ds ...

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Q: 23. Find the product. (-3x - 7)(5x + 8) 24. What's the equation of a horizontal line through the poi...

A: Q22,24,25 asked and answered.

Q: Let f be a C function on [-7,7]. Prove that the Fourier coefficients of f satisfy K | an |< | bn |< ...

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Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres ...

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Q: 13. Find the slope-intercept equation of the line pas sing through the point 2. 1) with a slope of m...

A: Q. 13 we have to find the slope intercept equation of the line passing through the point (2, 1) with...

Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n n3 + n2 +1 n=1 converges or diverges...

A: We have to find the given series is convergence or divergence.

Q: If S is a region in the xy-plane whose moment about the x-axis is given by the definite integral 1 (...

A: Given S is the region in xy plane whose moment about x-axis is Mx=12ρ∫01(x-x2)dxwhere ρ is density o...

Q: Skill-Building Activity Use power series to solve the differential equation. 2. y' = x?y

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Q: 1. Let f and g be continuously differentiable functions. PROVE: div( f vg - g v f) = fag -gAf Hint -...

A: Given that f and g be continuously differentiable functions. we have to prove that         divf∇g-g∇...

Q: 3. Use the Comparison Test to determine if the series Σ 5n Cos 2n n3 + n2 +1 n=1 converges or diverg...

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Q: Sólve the following differential equations: Homework V1-3x 1 dx+ sin y (a) (b) xy+x Inx=1-3x Cos 2y+...

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Q: Find the value of a + b + c + d. (Answer must be an integer) The Differential Equation 2y"' + 3y" – ...

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Q: If T is a region in the xy-plane whose moment about the y-axis is given by the definite integral My ...

A: If T is the region in xy-plane whose moment about y axis is given as My=ρ∫01(x-x2)dxwhere ρ is densi...

Q: A cherry with a temperature of 25 °C was submerged in a punch of vodka of temperature 5° C. After a ...

A: Given A Cherry with a temperature of 25∘C was submerged in a punch of vodka of temperature 5∘C After...

Q: 10 x2 +9 dx 5

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Q: Which of the following shows finding the area of an area outside the curve Y- 36 sin (20) and within...

A: Please see the attachment

Q: onsider the function f defined by f (x) =| sin x |, for - T < x < T. a) Find the Fourier series of f...

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Q: Compute the average value of f(x, y, z) over the region W. S(x. y, z) = 24xysin(5zz) W : [0, 1] x [0...

A: Average value of f over W =1volume of W∫∫∫W f(x,y,z) dV

Q: please send handwirtten solution Q2

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Q: Using Max-min composition, find relation between R and S: Уг Уз X1 [1 1 0 0 0 1 Z1 Z2 У1 [о 1 S = y2...

A: Solution 2. Given that               y1y2y3R=x1x2x3110001010 and                z1z2S=y1y2y3011011 L...

Q: 1. Find the Maclaurin Series for X COS x.

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Q: -Sy =D0

A: Given that y'''-8y''+6y'-5y=0. We have to find a method so that we can solve the above equation.

Q: (3) Evaluate the flux integral where S is the surface given by 22 =1 +y°, 0<= s 4, oriented upwards ...

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Q: Answer the following questions: 1. Bring out the different uses and the application of Business Math...

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Q: Find a basis for the subspace of R4 spanned by S. S = {(5, 9, −5, 53), (−4, 5, 4, −5), (8, −4, −8, 1...

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Q: 6) The graph of f (x) on the interval [0, 1] is shown below. Use a midpoint rectangle approximation ...

A: Given: Graph of a function, To find: Area of shaded region using midpoints of 5 intervals of equal ...

Q: A basketball team sells tickets that cost $10, $ many tickets of each kind have been sold?

A: Given, a basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold...

Q: A parallelogram has sides AB, BC, CD, and DA. Given A(1,-1,4), C(a. b.c), the midpoint M(1. 0,9) of ...

A: The complete solutions are given below