Show that
∫^[infinity]_1 1/x^p dx
converges if > 1 and diverges if p≤1.

Step-by-step explanation:

Consider the integral

for various values of p

CaseI:p =1 Then integral is ln x and for infinity this value diverges so diverges

Case 2: p<1

The integrated value would be

Since P <1 numerator x will have positive exponent and when infinity is substituted this will diverge

Case 3: p >1

will have x with negative exponent. So when x = infinity this value becomes 0 thus making the integral to converge

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.

you should talk someone who owns the website about it. you did not deserve to have all that hard work and time taken away. id watch videos of little puppies to cool you down, and maybe some nacho cheese doritos.