- #1
loreberto911
- 4
- 0
Hi everybody, I have this function to study
##\frac{(x+1)}{arctan(x+1)}##
I need the limit to infinity,it's oblique and I have to find q,from y=mx+q.
so
q=lim(x->inf) ##\frac{(x+1)}{arctan(x+1)} -2x/\pi##
I don't know how to solve it.the limit gives infinity to me.but calculators online give
##q=\frac{2(2+\pi)}{\pi^2}##
I can't use laurent series
thanks!
Ok I post everything I know, the function is
##f(x)=\frac{(x+1)}{arctan(x+1)}##
I have to do a normal study function, the limit the function to +- inf is inf so I have to find the oblique limit.
the formula is
lim x->inf f(x)-mx-q=0
m=lim x->+-inf f(x)/x=lim ##f(x)=\frac{(x+1)}{xarctan(x+1)}##=##\frac{2}{\pi}##
q= lim x->+-inf f(x)-mx = ##f(x)=\frac{(x+1)}{arctan(x+1)}## - ##\frac{2x}{\pi}##
=##\frac{\pi x+\pi-2x atan(x+1)}{atan(x+1)\pi}## =inf
but q has to be ##q=\frac{2(2+\pi)}{\pi^2}##
##\frac{(x+1)}{arctan(x+1)}##
I need the limit to infinity,it's oblique and I have to find q,from y=mx+q.
so
q=lim(x->inf) ##\frac{(x+1)}{arctan(x+1)} -2x/\pi##
I don't know how to solve it.the limit gives infinity to me.but calculators online give
##q=\frac{2(2+\pi)}{\pi^2}##
I can't use laurent series
thanks!
Ok I post everything I know, the function is
##f(x)=\frac{(x+1)}{arctan(x+1)}##
I have to do a normal study function, the limit the function to +- inf is inf so I have to find the oblique limit.
the formula is
lim x->inf f(x)-mx-q=0
m=lim x->+-inf f(x)/x=lim ##f(x)=\frac{(x+1)}{xarctan(x+1)}##=##\frac{2}{\pi}##
q= lim x->+-inf f(x)-mx = ##f(x)=\frac{(x+1)}{arctan(x+1)}## - ##\frac{2x}{\pi}##
=##\frac{\pi x+\pi-2x atan(x+1)}{atan(x+1)\pi}## =inf
but q has to be ##q=\frac{2(2+\pi)}{\pi^2}##
Last edited: