Please help me understand the following 3 problems

[Kryzen]

Hey guys, I am having some trouble understanding how to solve the following three problems. I am basically stuck on where to start these problems more then anything.

1) show that the following integral: dx/[(x+1)^(3/2) + (x-1)^(3/2)}.. can be transformed into x=1/2[t^2+ (1/t^2)]


2) find the area of the region bound by the graph y^2= X^2(1-x)/(1+x) x=0 to x =1

3) using mathematical induction, show that lim as x->infiniti [p(x)/e^ax] where P(x) = n/sum/k=0 of (asubk)x^k exponential functions dominate polynomials.
(sorry about the value of P(x) not sure how to write that in forums)

Thank you guys, your help is much appreciated.

 

[HallsofIvy]

Hey guys, I am having some trouble understanding how to solve the following three problems. I am basically stuck on where to start these problems more then anything.

1) show that the following integral: dx/[(x+1)^(3/2) + (x-1)^(3/2)}.. can be transformed into x=1/2[t^2+ (1/t^2)

Rationalize the denominator

2) find the area of the region bound by the graph y^2= X^2(1-x)/(1+x) x=0 to x =1

For x positive \(\displaystyle y= x\sqrt{\frac{1- x}{1+ x}}\). Integrate from 0 to 1 to get the area above y= 0. Because the original formula was for \(\displaystyle y^2\), double the integral to get both above and below the x-axis.

3) using mathematical induction, show that lim as x->infiniti [p(x)/e^ax]

Prove it is what? You've left out the critical part of the problem. That it converges?

where P(x) = n/sum/k=0 of (asubk)x^k exponential functions dominate polynomials.
(sorry about the value of P(x) not sure how to write that in forums)

Thank you guys, your help is much appreciated.

Do you know what "exponential functions dominate polynomials" means?