If m is a positive integer and x > 1, then show that (−1)″ xm+1 dm m! dxm 2F₁ m+1 m+2 2 2 ;1; + ²) = 1 H

Q: 3. Let V = R[x]4 (polynomials of degree at most 4). Let T: V → V be the linear map given by T(ƒ) =…

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Q: The following statements are about the chromatic number x(G) and the chromatic index x'(G) of…

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Q: - Evaluate the limit lim and justify your answer. S ng"-3 sin - dr 1 + xn n

A: As per the question we are given an improper Integral whose integrand is a functional sequence. And…

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Q: A company's marginal cost function is C'(x) = = 9 √x Find the total cost of the first 64 units (from…

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Q: Find Cartesian equation for the curve represented by the parametric equation x=et-6, y = e²+

A: To find the Cartesian equation we have to write a equation in terms of the variable x and y only. I,…

Q: 4. Find MacLaurin's series (i) using the known function series (see slide 30 from the Lecture Notes…

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Q: The first derivative of a continuous function y = f(x) is y' = (12x-10x²) (3 - x)². Find y'' and…

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Q: Identify the inflection points and local maxima and minima of the function graphed to the right.…

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Q: = would converge. n=1 9" (x-6) n+6

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Q: dt -We can get the roots m² +Gm +8 -0 corresponcting by using it's ^ auxiliary equation

A: Here we find characteristics roots. Complementary Solution  Particular solution.

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Q: You deposit $4000 each year into an account earning 5% interest compounded annually. How much will…

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Q: 5. Let X be any finite set and define the relation R on P(X) by R = {(E, F) ||E| = |F|, E, F =…

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Q: Use the function Q(p) = 3plnp² to answer the following question.

A: We use the properties of derivative to find the answers for given questions.

Q: (Linear Functions MC) An online streaming service that offers TV shows, documentaries, and movies…

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Q: -prime and m = mmm Then f(x) = 0 (m) has a solution if the congruences f(x) = 0 (m) has a solution.…

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Q: Domain:[-3,0) U (0, 1) U {3U (, ∞0) Range: [-6, -3) U (-3,-2) U{-1U (1, ∞)

A: simplify what it means after the third U in both answers . like write it in another way...

Q: Y" - 5y" + 3y' +9y = 0, y (0) = 0, y'(0) = -1, y" (0) = 1 (use Laplace Transforms)

A: To solve the given initial value problem of the differential equations Using the method of the…

Q: Find the final amount of money in an account if $3,900$3,900 is deposited at 7%7% interest…

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Q: The payment necessary to amortize a 4.4% loan of $95,000 compounded annually, with 4 annual payments…

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Q: 5) Using transformation and integration, find the area of the region that is enclosed by the ellipse…

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Q: 5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in- terval I =…

A: Used the definition of continuity.

Q: Radio direction finders are placed at points A and B, which are 4.17 mi apart on an east-west line,…

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Q: 2. Let M2x2 (R) be the set of all 2 x 2 matrices (with real number entries). That is a b {[%] | a,…

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Q: G is a finite group and Z is its centre, then class equation of G is expressibi o(G) o(G) = o(Z) + E…

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Q: Select all the convergent series a. Στη 1 b. n=1 C. ΣΤΑ 1 3" n! (-1)" n2

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Q: f(x) = x² + 2x - 8

A: The given function is, fx=x2+2x-8. (A) rational function g(x) that is opposite of the given…

Q: 2.1.3 .5 -.1 .4 .8 2 3. .4 .4

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Q: Write the equation in logarithmic form. 10³ = 1000 Ⓒlog 1000 = 3 Ⓒlog 3 = 10 1000 = log 3

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Q: 4. Evaluate the iterated integral: CIE dyda.

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Q: Sketch the graph of the function and check the graph with a graphing calculator. Before doing so,…

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Q: Show that (n) ‡ 14 for all n ≥ 1.

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Q: When the students in the class lined up four to a row, there was one left over; when they lined up…

A: The hint clearly says to use the Chinese Remainder Theorem and we shall use it. First we shall…

Q: Evaluate √(x + √1-a²)da by interpreting in terms of areas.

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Q: for Suppose the vector field v(x, y, z) = 3zi+ (2x − 3) j+ 4x k represents the velocity field of a…

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Q: The length of a rod is 15 m and the measure of the linear density at a point is a linear function of…

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Q: Compute the amount of work done by the force field F(x, y, z) = (x² − z², lny, xz) in moving an…

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Q: Suppose that f:[0,2]→R is differentiable, f(0) = 0, f(1) = 2, and f(2) = 2. Draw a sketch and cite…

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Q: Prove that the function f: R → R: x x² + ax + b where a, b E R is continuous at every c E R.

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Q: 1. Ytt = 4yxx, 0 0; y(0,1)= y(л,t) = 0, y(x,0) = sin 2x, yt (x, 0) = 0 10

A: Since there are two questions, therefore find the solution of the first question.

Q: Find the area of the shaded region. 4 3 2 1 +++++ -1 -1 -2 1 y = x^0.5 + 1 TN 2 Upload Choose a File…

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Q: Evaluate the following summations. (e) Σ2000 (2+3k). k=0 200 (f) Σ% 2 · (1.01).

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Q: 2. Let R be an integral domain (a) Define prime element and irreducible element (b) Prove every…

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Q: 1. Define f(x) = & Prove that f: R→ R is continuous. if z 20 -2² if r ≤0

A: Given: fx=x2if x≥0-x2if x≤0 Using sequences we have to prove that f:R→R is continuous.

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: 3) d²x cl+²2 Now + 8clx dt (D² + 80 +25)X = 10 ult) u(t)=0 when, + 20 2 (0² + 80 +25) x = 0…

A: For first part, We know that series of (1+x)-1 = 1 + x + x2 + ... Using this we expand where x =…

Q: Use the Newton-Raphson iterative method to find the root of the function ƒ(x) = x³ + x² + 4x + 2in…

A: The Newton-Raphson iterative method to find the root of the function f(x) is given as follows: xn+1…

Q: Estimate the area under the graph of the function f(2)=√√2+5 from z=-3 to z = 4 using a Riemann sum…

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Q: Prove each of the following statements using mathematical induction. (d) Prove that for any positive…

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