Let H = Span{1+x,1+x², 3+x +2x², 2 + x + x²}. what is dimH?

Q: Laplace and Inverse Laplace Transform 1. L{ †3 – 12 + 5t + 2}

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Q: Find the solution of the following IVP using the characteristic method : u + uu= y у , и(1,у) %3D Зу

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Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

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Q: 300r Integrate numerically: f (x) = 1+e from 0 to 10 using 5-segment trapezoidal rule. Round-off the…

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Q: +00 22n Σ (2x 1)". Vn2 +1 onsider the power series n=1 1. Use alternating series test to show that…

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: 4. Apply to the initial value problem y' = -ry + 1, y(0) = 0 three steps of the Picard-Lindelöf…

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Q: Evaluate the Inverse Laplace Transform 2 s+s+ 3 F(s)=

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Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: too Consider the power series > 22n (2.r- 1)". Vn? +1 n=1 3. Determine the radius and interval of…

A: A series will be  conditionally convergent if and only if the series  is convergent, but the series…

Q: 4 - 2v2. R

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Q: 1 11 a Let A = -4|. Find a QR-factorization of A. If R then -1 -1 the value of a is the value of b…

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Q: Two foods contain proteins, carbohydrates, and fats. Food A costs $1 per pound and contains 30%…

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Q: Find volume of body bounded by z = x-y from below and z = x + y from Above inside y = x ,y 2.

A: Volume bounded by the region

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: 2. Using triple integral to find the volume of a solid whose base is the region in xy-plane (z = 0)…

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Q: Evaluate the Inverse Laplace Transform F(S)=T51)² -2

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Q: If C is the circle |z|=4 evaluate Sf(z)dz for each of the following functions using residue. (a)f(2)…

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

Q: Determine the 3rd degree Maclaurin polynomial for f (x)= cot"(x) cot"EI) then use this to estimate…

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Q: Eva‎luate the ite‎rated do‎uble integr‎al ∫ 3−1 ∫ 0√(3−y) e12x−x^3 dx dy by chan‎ging the or‎der of…

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Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: In x2/25+ x2 dx , we let x = 5sine. A True B) False

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Q: What present value P amounts to $280,000 if it is invested at 5%, compounded semiannually, for 19…

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Surface are of the surface z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the projection of the…

Q: 3. 2х, — х, = 2 х, — Зх, + х; 3 — 2 -x, + x2 - 3xz - 6 %3D

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Q: Example 7 Sketch the curves (a) r 1 (b) @ = 4. %3D in polar coordinates.

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Q: Show that the sequence {- 2.4...(2n) }tinf converges by the Monotone 3.5...(2n+1)'n=1 Convergence…

A: Here I have applied the Monotone Convergence Theorem to show that the given sequence is convergent.

Q: Consider the function g(x, y) = x³ – 4x + ye" – In y. a. Find all critical points of g. At each…

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Q: (1) Find A, B, C, make the algebraic precision of the quadrature formula [f(x)dx = - Af (0)+ Bf…

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Q: What is the volume generated by revolving about the x axis the area bounded by the y = 2x +1, y = 0,…

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Q: Determine whether the improper integral converges or diverges. If converges, find the value. In x?dx

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Q: Use polar coordinates to evaluate sin (a² + y²)* dA, R where R is the region enclosed by the curves…

A: Here if we put limits in order dr dθ, then the given integral can not b evaluated so we need to put…

Q: j5)(8e1° )

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Q: А - (BUC) — | (А — В) UC (А — В) U (A — С) | О Оption 4 Оption 1 (А — В)n (A — С) (А — В — С)

A: 1. As by distributive property A - (B ∪ C) = (A - B) ∪ (A - C) Hence Answer: Option 1 (A - B) ∪ (A -…

Q: Find the Volumes for the fallowing solids whose heights ave defined by ECX y) and bases are the…

A: Volume bounded by the region

Q: Σ (-1)" (2n + 1)! Given: sin x = ,2п+1 for x E R n=0 (-1)"(2n + 1) Compute the exact value of the…

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Area of the surface given by the equation z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the…

Q: (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to…

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Q: Write the integral that would be used to find the area bounded by y =x² + 1, y = x – 2, x = -2 and x…

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Q: +00 (5 – 4(ln n)³)" Σ (V3 . In n)3n n=2

A: Given series is ∑n=2+∞(5-4(ln n)3)n33·ln n3n

Q: 3 Through polar coordinates, evaluate S S cos(x² + y²)ā dA, R where R is the region enclosed by…

A: The given question is related with evaluation of a double integral. We have to evaluate ∬R cosx2 +…

Q: (a) If an 2 0 for all n E N, then an does not converge conditionally. n=1 (b) If the power series >…

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Q: Let H = Span{1 +x²,1+x,1+x + a²,1+2x – 2x²}.What is dim H?

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Q: The locations of a spider (S) and its prey (P) are shown on the box below. The pider is on the front…

A: We will place the box on xyz co ordinate system , and then find co ordinate of points S and P .…

Q: Given: sinx (-1)" (2п+1)! 2n+1for x ER (-1)"(2n+1) ,2n+1| Compute the exact value of the sum -0 4"…

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Q: Consider an = tan-l n • Determine if the sequence {an}=1 converges or diverges. • Is the series > an…

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