A) γ(n) =∫[infinity]0tn−1e−tdta)show that γ(n+ 1) =nγ(n) using integration by parts. b) show that γ(n+ 1) =n! , wherenis a positive integer, by repeatedly applying the result in parta)c) compute γ(5).d) prove what the value of γ(12) should be by evaluating the gamma function forn= 1/2 and usingthe fact that∫[infinity]0e−u2du=√π2.

a. Integrate by parts by taking

Then

We have

and so

or, replacing , .

b. From the above recursive relation, we find

Now,

and so we're left with .

c. Using the previous result, we find .

d. If the question is asking to find , then you can just use the same approach as in (c).

But if you're supposed to find , we have

Substitute

Then

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet

the radius is 2 times the diameter.

step-by-step explanation: