G find all the values of p for which the following functions are improperly integrable on the indicated domain. be sure to prove your claims, ie show that it is improperly integrable for those numbers p, but is not for other numbers 1.f(x)=1/x^p on i =(0,1) 2. f(x) = 1/(x(lnx)^p) on I = (e, inf)

1. In order to make the integral improper    must be 1.

2. In order to make the integral improper    must be 1.  

Step-by-step explanation:

Using the rules of integration we get that for

Therefore in order to make that integral improper    must be 1.

If  p = 1     then you would have a 1/0  indeterminate form.

2.   Using the of integration, specifically substitution we get that for

For    we would have

And the problem is the same.  If     we would have a 1/0 indeterminate form.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500