Could someone help with these beginner level math problems?

[tädif]

Could somebody help !?

I really appreciate, if somebody could help me with these tasks, I am beginner and really need fast help. Also, as my mothertonque is not English, some mathematical terms may be wrong, hope you understand.



1. Function y=ln (x+10/x-8)+80

a)find domain, b)asymptotes equations, c)Extremums, d)grow and decline areas, e)curvature and concava areas, f)point of inflections



2.Function: z=xy+40x, a) find Extremums in condition: x^2+y^2=256

b) control sufficiency, c) designate type, d) calculate the value of function



Thank you!

 

[foxjwill]

for "grow and decline areas", we would usually say "intervals with positive and negative slope"; for "curvature and concava areas", we'd usually say "concave up and concave down areas". The plural of "extremum" is "extrema", although many native English don't know this!

Anyway, could you show your work?

 

[tädif]

1.a) (x+10/x-8)>0
x-8=(not equal)0
(x+10)(x-8)=0
x1=-10, x2=8
Domain: ]minus Infinity;-10[compound]8;infinity[ ?
b) have no idea how to find asymptotes equations
c)i got derivative 2/[(x+10)(x-8)]
then solved the equation and got x1=-10 and x2=8
but when analyzing the extremum places then i got that both are not suitable becuse you can't take ln0?, but there should be extremum places.