(a)
The correct match for the graph of the first
(b)
The correct match for the graph of the first
(c)
The correct match for the graph of the first
(d)
The correct match for the graph of the first
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Calculus: An Applied Approach (Providence College: MTH 109)
- IV. (a) Write using summation notation: 1 + 1 + 1 + 32 3 + 1 3n (b) Transform the summation by making the specified change of index variable k to variable j using the relationship j=k-1: 7 E k(k+2)(k-3) k=1 Write out the first four terms of the summation below.: Include at least 4 terms j (-1) = j-1 4 (-2) = j= 1 (d) Compute the productarrow_forward3. (a) Find a closed formula for the generating function A(z) of the sequence an = (3n - 7) (-2)". (b) Find a closed formula for the generating function of the sequence Sn = ao + a₁ ++ an, where an is defined in part (a). (c) Use your answer to part (b) or otherwise, to calculate the sum ao + a₁ ++ an, where an is defined in part (a). (d) Write the generating function B(z) of the sequence bn = (n + 1) 3 ao+n3n-¹a₁ +...+ an in terms of A(z) (you do not need to use any explicit form of A(z)).arrow_forward-k + 4 k2 – 11 Consider the series (a) Find the first three terms in the sequence of partial sums. Write each term as a fraction in lowest terms (b) True or False: The Divergence Test tells us that the series diverges? Explain your answer.arrow_forward
- use A=200arrow_forwardConsider the following. 4(0.8) - 1 n = 1 (a) Find the sum of the series. Sn = 20 (b) Use a graphing utility to find the indicated partial sum and complete the table. (Round your answers to four decimal places.) n n 5 x 10 20 50 100arrow_forwardΣ (²-2) for j=1 to 50. The summation equalsarrow_forward
- (10k - 12)- (7 – 4n) x > (-6m) 22.Evaluate the given series k=3 n=2 m=1 O A. -108 O B. -52 O C. 3574 O D. -3482arrow_forwardSuppose you want to type sequences of vowels (that is, the letters a, e, i, o and u). However, the e key on your keyboard is defective and every time you press it, it outputs ee instead of just e. Let yn the number of sequences of length n you can type in this way. (i) Find yo, Y1, V2. (ii) Write a second-order difference equation for the value of yn. (iii) Solve the difference equation.arrow_forward(21) Determine if the sequence if convergent. Explain your conclusion. n²-1 = n²+8 (a) Cn 1 (b) cn = 20n²+1 (c) Cn - 0.1.n³-100 n²+3 (d) cn = (e) Cn = COS el/n³ ㅠ 2narrow_forward
- Rewrite -ln(3)+ln(4)-ln(5)+...+ln(20) using summation notation.arrow_forward(-1)" (4 – ) for every (3) Let (xn) be the sequence in R defined as xn n E N. Does (xn) converge? Give reasons for your answer. (4) Let A be an open subset of RP, and let (xn) be a sequence in RP which converges to a point x E A. Show that there exists an N E N such that xn E A for all n > N.arrow_forward2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for calculating the terms of the sequence (Pn) recursively defined by PnPn-1-f(p-1)- for all n>2, where Po= 1 and p₁=0.8 and where the function f is given by f(x) = sin(0.57x) - 0.28 (replace po and pi in the program with the corresponding values given above, and replace f(x) and f(Y) with correct expressions representing the values of the function f given above; say, f (x) should be replaced with Xxsin (0.57 x X ) - 0.28 Po X PLY f(x)→ E Y→ X F→ E C→ Y f(Y) → F Y FX (Y-X) + (F-E) → C Pn-1-Pn-2 f(pn-1)-f(pn-2) (1) n (3) 0 1 2 Prior to studying the above program, it is a good idea to start with creating your own program for calculating the terms p, in a familiar programming language, and/or in Excel (OpenOffice), and then to compare your program with the program for a sci calculator. (ii) Execute the program for a sci calculator to get the terms P2, P3, in it RADIAN mode). Present the results…arrow_forward
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