Find the value of ſ (2x – x³) dx by evaluating it as the limit of sums.

Q: Determine for what values of k the integral ∞∫1dxxk(k>0,k≠1) converges.

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Q: Evaluate the upper sum for f(x) = 1 + cos - ASXST Wwith n = 6.

A: GIVEN: f(x) = 1 + cos (x/2)

Q: Evaluate the Riemann sum for f(x) = x3 + x2 − 6x + 2, taking the sample points to be right endpoints…

A: I have used formula for Riemann Sum

Q: Prove that if r >1 then f r" dx converges to 1

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Q: To compute (1+ æ) dæ using the limit definition, what is the Riemann sum? n 2 4+ 4+ 4 +1 n

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Q: The diagram below shows upper and lower sums for the function 3. f (a) = 2/1- ai %3D using 4…

A: Given Function f(x)=21-x32 Given Interval=[a,b]=[0,1]; n=4 subintervals ∆x=b-an=1-04=0.25 so, the…

Q: If  f(x) = 5x2 − 6x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

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Q: Let f and g be as in the figure, we may deduce that if I g(x)dx converges then

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Q: (x + n)² Show that h„(x) converges poimtwise to f(x) = 1, V x e [1, 00). %3| x² + n²

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Q: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that…

A: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that the…

Q: ) Find the limit superior and limit inferior of each of the following sequences: (a) X = (xn) =…

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Q: for r20. Exercise 5. Consider the sequence (fn)n defined by fn(x) D 1. Find f(x) = lim,+o fn(x).…

A: We have to solve given problem:

Q: Find Limit of .... as n approaches infinity    an= ((-1)^n)/n^2 bn = e^n /5^(2n)) cn = ln(n)/n^5

A: Definition used -           limn→∞(a)n=0a<1∞a>1           We can use the L'hospital rule when…

Q: Find the constant term in the expansion

A: We have to solve the problem

Q: For each n E N, consider xn n == X with x ER+. Define the sequence {gn} by 1 +2' 8n(x) = f(xn) (a)…

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Q: 2x Write the integral e eat d x as the limit of Riemann sums using the right endpoint rule. That is,…

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Q: Find the Riemann Sum for the function f(x)=12x+1 and the partition {0,2,5,8} using the sample points…

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Q: a) Evaluate the Riemann sum for f(x) = 3.x² – 6x+1, taking the sample points to be right point and a…

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Q: H.W Given a sequence x(n) for 0sns3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) 0, compute its…

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Q: 2. s) Let x1 = 1 and define rn+1 = v3+2x, for n E N. Show that the sequence (xn) converges and find…

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Q: If f(x) = 3x2 . - 4x, 0 < x < 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: The function is given as , fx=3x2-4x  a=0 , b=3 , n=6 R6=?

Q: 1 d.x x In (ex)

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Q: If f(x) ≤ g(x) for all x in [a, +∞o) and converges. •+∞ f(x) da converges, then [*** g(x) dx also

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Q: If f(x) = 5x² – 2x, 0 < x < 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

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Q: If f(x) = Vx – 2, 1 < x < 6, find the Riemann sum with n = points. 5, taking the sample points to be…

A: Given, If the function f(x)=x-2 ,1≤x≤6 with n=5

Q: Find the limit of s(n) as n o. 1n(n + 1) | s(n) n2 8

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Q: If f(x) = 2x - 7,0 < x < 3, find the Riemann sum with n = 6, taking the sample points to be…

A: Given:- f(x) = 2x2-7 , [0, 3]  To find:- Riemann sum with n = 6 , taking the sample points to be…

Q: Compute the definite integral as the limit of Riemann sums. 21) [ x3 dx -3 81 81 C)- 2 A) 27 D) 0 4

A: let I=∫-33x3dx claim- to find the definite integral using limit of riemann sum let fx=x3 where a=-3…

Q: 9n + 2" 46. Prove the divergence of n=0

A: Given series  ∑n=0∞9n+2n5n where an=9n+2n5n.

Q: Q2/ Find the final value of the sequence {xk} with Z transform 4z2-z F(z) %3D 2z2-3z+1

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Q: Suppose that the function f:R → R be differentiable and that {xn}is a strictly increasing bounded…

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Q: (a)Give the pdf of X. (b)Find P(X > 15) using the relevant summation.

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Q: We define an arithmetic sequence of functions: fn: [1,0) → R recursively as: fi(x) = Vx, Vx € [1, 0)…

A: Given fn:[1,∞)→ℝ recursively as: f1x=xfn+1x=x+fnx for all x∈[1,∞). (a). Let x∈[1,∞), therefore:…

Q: In = Vn (Vn +1- vn

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Q: If f(x) = 3x2 - 4x, 0 sxs 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: Given f(x) =3x2 - 4x , a=0, b=3 and n=6 Now calculate f(x)

Q: If f(x) 5x2 – - 6x, 0 < x < 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

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Q: Let fn(x) = x¹(1+x¹)−¹. Use the uniform norm to determine if the sequence (fn) uniformly converges…

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Q: 1. f(x) da converges, then If f(x) ≤ g(x) for all z in [a, +∞o) and converges. g(x) dx also

A: Given

Q: 1) For the function f(x) = 10 - 4x2 , find a formula for the lower sum obtained by dividing the…

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Q: Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0, 4].…

A: Given limit is                        limn→∞4n4n+8n+12n+...+4nn Again…

Q: For the function f(x) = 5x + 3, find a formula for the upper sum obtained by dividing the interval…

A: Given: f(x)=5x +3, interval [0, 3] To find the formula for upper sum obtained by dividing given…

Q: 1 and yn+l = V2 + Yn for n > 1. Show (ym) is monotone, and Let yn bounded, and compute its limit.

A: Here, we have a recurrence relation for the sequence. by using that we need to check the sequence is…

Q: Show that g(n) = 3" + 1010" is asymptotically bounded above by f (n) = 4".

A: Given, gn=3n+101010fn=4n Now, divide gn by fn we get,…

Q: Let f(x)= (-1)* x« (2k)! ,6k Find [f (x)dx. Write in summation form. k =0

A: Here is the solution of the given problem.

Q: 5b) Let f (x, y(x)) = y(x) + 1 and y(0) = yo = 2. Use Picard-iteration and induction to show that YN…

A: Please go through the solution.

Q: Use series to evaluate the limits

A: Given: To find:  lim t→0  1- cos t - (t22)t4Formula:  cos t…

Q: The sequence a, n – vn+ lvn+3 converges to the limit A) -3 B) -1 C) 1 D) +2 E) -2

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Q: nx +n² +x? Explore the uniform convergence of the functional sequence f.(x) = n² +x? on the set E =…

A: Differentiate the function fnx=nx+n2+x2n2+x2 with respect to x, and solve the equation fn'x=0. Apply…