a. To explain: The number of bacteria in the dish after 10 hours and after n hours .

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Answer 1

Question

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

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Exercises Evaluate the following limits. 1. lim cot x/ln x +01x 2. lim x² In x +014 3. lim x* x0+ 4. lim (cos√√x)1/x +014 5. lim x2/(1-cos x) x10 6. lim e*/* 818 7. lim (secx - tan x) x-x/2- 8. lim [1+(3/x)]* x→∞0

In Exercises 1 through 3, let xo = O and calculate P7(x) and R7(x). 1. f(x)=sin x, x in R. 2. f(x) = cos x, x in R. 3. f(x) = In(1+x), x≥0. 4. In Exercises 1, 2, and 3, for |x| 1, calculate a value of n such that P(x) approximates f(x) to within 10-6. 5. Let (an)neN be a sequence of positive real numbers such that L = lim (an+1/an) exists in R. If L < 1, show that an → 0. [Hint: Let 1111 L

iation 7. Let f be continuous on [a, b] and differentiable on (a, b). If lim f'(x) xia exists in R, show that f is differentiable at a and f'(a) = lim f'(x). A similar result holds for b. x-a 8. In reference to Corollary 5.4, give an example of a uniformly continuous function on [0, 1] that is differentiable on (0, 1] but whose derivative is not bounded there. 9. Recall that a fixed point of a function f is a point c such that f(c) = c. (a) Show that if f is differentiable on R and f'(x)| x if x 1 and hence In(1+x) 0. 12. For 0 л/2. (Thus, as x л/2 from the left, cos x is never large enough for x+cosx to be greater than л/2 and cot x is never small enough for x + cot x to be less than x/2.)

Answer 2

Question

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

Answer 6

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

Answer 7

Chapter 1, Problem 7NT

To determine

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

Answer 8

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

Answer 9

To determine

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

a. To explain: The number of bacteria in the dish after 10 hours and after n hours .

a. To explain: The number of bacteria in the dish after 10 hours and after n hours.

b. To explain: The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.

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Chapter 1 Solutions

a.

To explain:

The number of bacteria in the dish after 10 hours and after n hours.

b.

To explain:

The growth after 10 hours and after n hours when the bacteria increases arithmetically. Comment on the difference in growth of a geometric sequence versus an arithmetic sequence.