Math 152 - sec 37,38,39 - workshop 07 Problem (1). Find whether each of the given sequences {an}=1 is converges or diverges. If it converges, п-1 find its limit. cw {rm} 2n3 – 3 (i) an = n1/n³ (a) 1+ n2 (е) ап V4n6 – 7n + 8 (:)" (j) an In(1+2e") l (b) 2n3 – 3 (f) an VAn6 – 7n + 8 (k) an (c) {vn+1- Vn} езn + 4 (g) an 2e2n (1)" 5n { п cos (2тп) (d) (h) an = Vn (1) an 2n -) Problem (2). Let m and n be integers such that n, m > 1. Let lim x" sin = Lm,n, if exists. п; х0 sin () (a) Evaluate lim (b) Show that Lm,n 1 when m = n. (c) Find Lm,n for n > m. (d) Find Lm, n for n < m. Problem (3). Let ƒ(x) = x² – 6. We set ao = 4 and define the sequence {an} recursively as follows: n=0 f(an) f'(an)" An+1 = An (a) Use your calculator to find the first ten terms of the sequence. (Hint: you may want to simplify the expression for an+1 before you begin your calculations.) Based on your findings, do you think this sequence will converge or diverge? (b) Make a careful sketch of the graph of y = f(x) together with the tangent line to y = f() at x = Then locate the term a1 on the x-axis. What do you observe? 4. (c) Based on your sketch in part (b) and your knowledge of calculus, what does this sequence "locate?" Explain.

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Chapter2: Second-order Linear Odes
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Problem 2 parts A, B, and C please

Math 152 - sec 37,38,39 - workshop 07
Problem (1). Find whether each of the given sequences {an}=1 is converges or diverges. If it converges,
п-1
find its limit.
cw {rm}
2n3 – 3
(i) an = n1/n³
(a)
1+ n2
(е) ап
V4n6 – 7n + 8
(:)"
(j) an
In(1+2e") l
(b)
2n3 – 3
(f) an
VAn6 – 7n + 8
(k) an
(c) {vn+1- Vn}
езn
+ 4
(g) an
2e2n
(1)"
5n
{
п cos (2тп)
(d)
(h) an =
Vn
(1) an
2n
-)
Problem (2). Let m and n be integers such that n, m > 1. Let lim x" sin
= Lm,n, if exists.
п;
х0
sin ()
(a) Evaluate lim
(b) Show that Lm,n
1 when m = n.
(c) Find Lm,n for n > m.
(d) Find Lm, n for n < m.
Problem (3). Let ƒ(x) = x² – 6. We set ao =
4 and define the sequence {an} recursively as follows:
n=0
f(an)
f'(an)"
An+1 = An
(a) Use your calculator to find the first ten terms of the sequence. (Hint: you may want to simplify the
expression for an+1 before you begin your calculations.) Based on your findings, do you think this
sequence will converge or diverge?
(b) Make a careful sketch of the graph of y = f(x) together with the tangent line to y = f() at x =
Then locate the term a1 on the x-axis. What do you observe?
4.
(c) Based on your sketch in part (b) and your knowledge of calculus, what does this sequence "locate?"
Explain.
Transcribed Image Text:Math 152 - sec 37,38,39 - workshop 07 Problem (1). Find whether each of the given sequences {an}=1 is converges or diverges. If it converges, п-1 find its limit. cw {rm} 2n3 – 3 (i) an = n1/n³ (a) 1+ n2 (е) ап V4n6 – 7n + 8 (:)" (j) an In(1+2e") l (b) 2n3 – 3 (f) an VAn6 – 7n + 8 (k) an (c) {vn+1- Vn} езn + 4 (g) an 2e2n (1)" 5n { п cos (2тп) (d) (h) an = Vn (1) an 2n -) Problem (2). Let m and n be integers such that n, m > 1. Let lim x" sin = Lm,n, if exists. п; х0 sin () (a) Evaluate lim (b) Show that Lm,n 1 when m = n. (c) Find Lm,n for n > m. (d) Find Lm, n for n < m. Problem (3). Let ƒ(x) = x² – 6. We set ao = 4 and define the sequence {an} recursively as follows: n=0 f(an) f'(an)" An+1 = An (a) Use your calculator to find the first ten terms of the sequence. (Hint: you may want to simplify the expression for an+1 before you begin your calculations.) Based on your findings, do you think this sequence will converge or diverge? (b) Make a careful sketch of the graph of y = f(x) together with the tangent line to y = f() at x = Then locate the term a1 on the x-axis. What do you observe? 4. (c) Based on your sketch in part (b) and your knowledge of calculus, what does this sequence "locate?" Explain.
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