(п-1)s2 (п-1)s* <σ< (25 – 1)0.24 (25–1)0.24 o< 39.36 12.40 0.187

Q: 9x Σ Suppose that Cnx". (15 + x) n=0 Find the first few coefficients. CO C1 C2 = C3 C4 = Find the…

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Q: (x+8)" 1) Find the interval of convergence of the series £(-1)" n6" n=| A) (2,14] B) (-14, –2] C)…

A: Since you have asked multiple questions, we will solve the first question for you ∑n=1∞ -1nx+8nn6n

Q: 1. Try to use the ratio test or the root test to determine if the following converge or diverge. If…

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Q: 2n2 +n+2 ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

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Q: (10-x²)y" +5xy' + y = 0 Solve the given ODE by the POWER SERIES METHOD, if x = 0 is an ordin point.

A: Given 10-x2y"+5xy'+y=0

Q: Q2/ choose the correct answer. (2) By using the iterative formula Xn+1 of the equestion X³ then the…

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Q: 5x Suppose that Cnx". (7 + x) n =0 Find the first few coefficients. CO C1 = C2 C3 C4 Find the radius…

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Q: Equating the coefficients of t" in the following series: æ(1+ 2n) Pn t" – (1+ n)Pn t"+1 – nPn t"-1]…

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Q: 4a) Perform the first three iterations of secant method to solve for x, given p = 3 and K = 0.05.…

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Q: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the…

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Q: 8 Let k(x) = |x|", n = 1,2, ... Is k differentiable for all x and every n? Find a formula for k' (x)…

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Q: (3) Find all p ER so that 3n² + 2n +1 n2p-1 + 137 n=1 converges. As always, your answer must be…

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Q: 1 ? < 40. The cubic x³ - 2x² - x + 1 has three real roots; one is negative. a. Find a rearrangement…

A: Solution :-

Q: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: (x-1)" Which are the values of for which the series n=1 n A. 0SX<2 O B. -1<x<1 O C.0<x<2 O D. -1sxs1

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Q: How do I calculate this? If Z~N(0,1), calculate Pr(1.55 < Z < 2.65)

A: Given that, Z~N(0,1)

Q: fun c tro n flL-x)= -fex) for EI odd n Suppose that f 1s odd for for tho n an {x/ -Lcx<L4. and…

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Q: d. The distance a freely falling body covers in the nth second is given by S(n)=d(n)-d(n-1). Show…

A: We know distance traveled by a freezing falling body in n seconds is given by  dn = 1/2(gn2)

Q: 2n²+3n 2 3) Prove (with an e - N proof): lim n-0o 3n2+8n+2 3

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Q: 3 Represent the function as a power series f(x) Cn x" (1 – 5x) n=0 Co C2 = C3 = C4 = Find the radius…

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Q: 2 3 () is equal to 1+ (x – 1) 1) Show that the sum of the series 1+ 2 +.. +... (x – 1)2 + (x –- 1)³…

A: We have to solve given problem:

Q: 6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies…

A: Laplace transformation: Laplace transform is an integral transform that converts a function of a…

Q: 5x Suppose that Cnx". (11 + x) n=0 Find the first few coefficients. Co C1 = C2 C3 = C4 Find the…

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Q: Which of the followings are true? 1. E1 \sin | converges by comparing with -1 II. E1 converges by…

A: Solution: (I) ∑n=1∞sin1n2 We know that sinx≤x Therefore, sin1n2≤1n2 Since ∑n=1∞1n2 converges, thus…

Q: dx -x 2-x Select one: O a. diverges to -x O b. diverges to x C. converges to -In(6) O d. converges…

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Q: Σ (-1)n+1 n3 n=1 11. Find an upper bound for the error in the above approximation |S – Sg].

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Q: n=1 B. E(-1)"- In n n=2 1 Inn c.(-1)"+1. n- Inn (-1)*+1. n + n=1 E.(-1)" sin(n) n=1 E(-1)"- n=2…

A: This is a problem of series calculation. based on the several available tests we can determine which…

Q: 1. Find the sum of the series (-1)" n² + 1° (The answer should be a real number). ANSWER: (T / sinh…

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Q: 2n Consider the series (-1)"b,, where (14n + 1)? - i? Which of the following is TRUE about the…

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Q: 4) Solve for y" + x²y' + xy = 0. Final answer must show the series until term of X7.

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Q: Q3. Express into partial fractions. Hence obtain the sum of the first 3 What is the value of S ? k=1…

A: Partial fractions

Q: 5n2 For E>0, there is a corresponding N such that -4/0 N. 4 +3 Then the value of L will be

A: Given function is , f(n)=5n24n+3

Q: 1z Suppose that (3+2) Find the first few coefficients. CO = C2 = C4= Find the radius of convergence…

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Q: 19. What are the first three terms of the series =1 CO ? 2%3D1 2 4 6 A. А. - 4 6. - - С. 1. - x3 -…

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Q: 5r² – 3)| -6,80 n=3 with Simpson's 3/8 rule. Find the approximate solution for

A: Simpson's 3/8 rule is: ∫abydx=3h8(y0+2∑ i=1n/3-1(y3i) +3(y1+y2+y4+y5+....+yn-2+yn-1)+yn)here y=f(x)…

Q: You are given that Cn (x – 3)" converges when x 8 and diverges when n=0 x = -3. Then the series > Cn…

A: Given power series: ∑n=0∞cnx-3n Also it is given that ∑n=0∞cnx-3n  is convergent when x=8 and…

Q: n 3 The numerical series ) n' log .3 n3 n=3 O converges to a negative number. O diverges to-00.…

A: Using limit comparison test

Q: 3n? is increasing. Find an upper bound. n2 +2 Show that an

A: Consider the sequence and check whether Sequence is increasing or not.

Q: 5x as a power series f(x) = >, c 00 Represent the function 6+ x Cnx" n=0 Co = C1 = C2 = C3 = C4 =

A: Let f(x) = 5x6+xf(x) = 5x6(1+x6)=…

Q: 2n2 +n+2 Σ ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

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Q: (x+6)k Find the interval of convergence of the series E=0 4k+3

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Q: lim In(")n %3D 7n00 n+1 Select one: O 2 -2 O-2 O e? 21

A: The given expression is limn→∞lnnn+12n

Q: 3" x" radius of conver gent for the series i : (n + 2)(n+ 1) (a)co (b)0

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Q: 15 E (2n – 1) n-1

A: We will use formula that 1+2+3+4+......+n= n(n+1)/2

Q: (-1)*+1 Vn 00 We would like to estimate the sum L of the series > n=1 with a partial sum Sn : L - Sn…

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Q: 5: A. Using convolution to find L¹ [(5+2)(s+4)

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Q: 5n+7 Find supremum of A :|n E N 4n+12

A: Given set isℝ A = 5n+74n+12 | n∈ℕ We know that a number u is the supremum of a nonempty subset S of…

Q: 6x Σ. Suppose that (7 + æ) n=0 Find the first few coefficients. Co = C1 = C2 C3 C4 Find the radius…

A: Given that 6x7+x=∑n=0∞cnxnfind the first few coefficientsand Radius of convergence R

Q: k2 Use the integral test to determine whether 2 1319)2 converges. (k3 + 9)2 k=1

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Q: (k-k) = O a. n O b. 6n +(n + 1)(2n +1) OC. 00 O d. (n + 1) O e. 4(n + 2) (n² - 1)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.