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Determine whether the following functions are continuous on the given interval. Show your complete solution.
1. Ζ(π₯)=β4βπ₯2 ;[β2,2]
2. Ζ(π₯)=3π₯2 βπ₯+5 ; (ββ,+β)
Determine whether the following functions are continuous at a given point. Show your complete solution.
1. Ζ(π₯)=3π₯2β4π₯+2atπ₯=2
2. Ζ(π₯)=π₯2β6π₯β3atπ₯=4
Determine whether or not the following are continuous functions.
1. Ζ(π₯)=5π₯+3 2. Ζ(π₯)=β4π₯+2
3. Ζ(π₯)=2π₯2 +π₯β3
4. Ζ(π₯)={2π₯β3 iΖ π₯β₯2 β2π₯ + 2 iΖ π₯ < 2
5. Ζ(π₯)={|π₯+2|iΖπ₯Gβ2 4 iΖ π₯ = β2
Do the following: (a) Construct the table of values; (b) graph the function; and (c) find the indicated limits.
1. limXβ+β 3X
2. limXβββ 4X
3. lim 1 X Xβ+β (3)
Evaluate the following limits.
1. limXβ+β 5X+6
2. limXβββ e4X+7
3.limXβββ(0.2)X
How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?Β
A study by Thienprasiddhi et al. (A-4) examined a sample of 16 subjects with open-angle glaucoma
and unilateral hemifield defects. The ages (years) of the subjects were:
62 62 68 48 51 60 51 57
57 41 62 50 53 34 62 61
Can we conclude that the mean age of the population from which the sample may be presumed to have been drawn is less than 60 years? Let alpha = 0.5
Independent random samples from normal distributions with equal variance of the amount of insider
trading during mergers by employees of investment banking firms (1) and brokerage houses (2) gave the
results listed in the accompanying table.
Investment Banking Firm 10 5 5 5 8 8 8
Brokerage House 6 0 5 2 2 3 3
(a) Find the 95% confidence interval estimate for the difference between means Β΅1 β Β΅2..
(b) Would you conclude that employees of Investment banking firms cause more insider trading than
their counterparts in Brokerage House?
the demand function π(π) and cost functions πΆ(π) of a commodity are given by the equations:
π=12000β60π
πΆ(π)=10000+4π,
where π and π are the price and quantity, respectively.Β
The total revenue function ππ in terms of π is:
a.
ππ =12 000β60π.
b.
ππ =π(12 000β60π2).
c.
ππ =12 000πβ60π2.
d.
ππ =12 000+60π2.
Conduct Hypothesis Testing Using Small-Sample Tests. Step- By- Step.
An experimental study was conducted by a researcher to determine if new time slot has an effect on the performance of students in mathematics. Ten randomly selected students participated in the study. Toward the end of the investigation, a standardized assessment was conducted. The sample mean was X=75 and the standard deviation s=20. In the standardization of the test, the mean was 65 and the standard deviation was 10. Based on the evidence at hand, is the new time slot effective? Use Ξ±=0.05.
