Numerical Analysis
10th Edition
ISBN: 9781305730663
Author: Richard L. Burden; J. Douglas Faires; Annette M. Burden
Publisher: Cengage Learning US
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Given the sample space:
ΩΞ
= {a,b,c,d,e,f}
and events:
{a,b,e,f}
A = {a, b, c, d}, B = {c, d, e, f}, and C = {a, b, e, f}
For parts a-c: determine the outcomes in each of the provided sets. Use proper set
notation.
a.
(ACB)
C
(AN (BUC) C) U (AN (BUC))
AC UBC UCC
b.
C.
d.
If the outcomes in 2 are equally likely, calculate P(AN BNC).
H-/ test the Series
1.12
7√2
by ratio best
2n
2-12-
nz
by vitio test
en
In Exercises 1-14, state whether each statement is true or
false. If false, give a reason.
1. The set of stores located in the state of Wyoming is a well-
defined set.
2. The set of the three best songs is a well-defined set.
3. maple = {oak, elm, maple, sycamore}
4{} cơ
5. {3, 6, 9, 12,...} and {2, 4, 6, 8, ...} are disjoint sets.
6. {Mercury, Venus, Earth, Mars} is an example of a set in
roster form.
7. {candle, picture, lamp} = {picture, chair, lamp }
8. {apple, orange, banana, pear} is equivalent to
{tomato, corn, spinach, radish}.
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- ding question ypothesis at a=0.01 and at a = 37. Consider the following hypotheses: 20 Ho: μ=12 HA: μ12 Find the p-value for this hypothesis test based on the following sample information. a. x=11; s= 3.2; n = 36 b. x = 13; s=3.2; n = 36 C. c. d. x = 11; s= 2.8; n=36 x = 11; s= 2.8; n = 49arrow_forward13. A pharmaceutical company has developed a new drug for depression. There is a concern, however, that the drug also raises the blood pressure of its users. A researcher wants to conduct a test to validate this claim. Would the manager of the pharmaceutical company be more concerned about a Type I error or a Type II error? Explain.arrow_forwardFind the z score that corresponds to the given area 30% below z.arrow_forward
- Find the following probability P(z<-.24)arrow_forwardExercises 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→∞0arrow_forwardIn 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 Larrow_forwardiation 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.)arrow_forwardConstruct a histogram for the spot weld shear strength datain Exercise 6.2.9. Comment on the shape of the histogram. Doesit convey the same information as the stem-and-leaf display? Reference: Exercise 6.2.9 is found in the image attached belowarrow_forward1. Show that f(x) = x3 is not uniformly continuous on R. 2. Show that f(x) = 1/(x-2) is not uniformly continuous on (2,00). 3. Show that f(x)=sin(1/x) is not uniformly continuous on (0,л/2]. 4. Show that f(x) = mx + b is uniformly continuous on R. 5. Show that f(x) = 1/x2 is uniformly continuous on [1, 00), but not on (0, 1]. 6. Show that if f is uniformly continuous on [a, b] and uniformly continuous on D (where D is either [b, c] or [b, 00)), then f is uniformly continuous on [a, b]U D. 7. Show that f(x)=√x is uniformly continuous on [1, 00). Use Exercise 6 to conclude that f is uniformly continuous on [0, ∞). 8. Show that if D is bounded and f is uniformly continuous on D, then fis bounded on D. 9. Let f and g be uniformly continuous on D. Show that f+g is uniformly continuous on D. Show, by example, that fg need not be uniformly con- tinuous on D. 10. Complete the proof of Theorem 4.7. 11. Give an example of a continuous function on Q that cannot be continuously extended to R. 12.…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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