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.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun