Monday, 8 May 2017

calculus - Question about steps/derivation regarding Laplace method.

I am reading something on the Laplace method of integrals and I don't understand part of it's argument. It gives the integral
43eλx2log(1+x2)dx
and finding the leading term of asymptotics for λ. It first argues



"Since only small |x|, such that |x|1λ1 are important,




log(1+x2)x2



I(\lambda)\sim \int_{-3}^4 e^{-\lambda x^2}x^2 \, dx \sim \int_{-\infty}^{\infty} e^{-\lambda x^2}x^2 \, dx \sim 2\int_{0}^{\infty} e^{-\lambda x^2}x^2 \, dx."



I'm really not following that argument at all. Any help would be appreciated.

No comments:

Post a Comment

real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

How to find \lim_{h\rightarrow 0}\frac{\sin(ha)}{h} without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...