Question

sa se determine ecuatia asimptotei

Answer 1

m= lim cand x->∞din (f(x)/x)=lim cand x->∞din (√(x²+3)/x(=

lim cand x->∞din (√((x²+3)/x²))=1

n= lim cand x->∞din (f(x)-1*x)=lim cand x->∞(√(x²+3)-x)=

=lim cand x->∞ din((√(x²+3)-x) (√(x²+3)+x)/√(x²+3)+x)=

=lim cand x->∞ din((x²+3-x²)/(√(x²+3)+x))=

=lim cand x->∞ din((3/(√(x²+3)+x))=3/∞=0

deci m=1 si n=0

atunci ecuatia asimptotei oblice y=mx+n devine y=x, prima bisectoare