Evaluate the following limits

Question

Evaluate the following limits. 

 

a) 

lim        sqrt(7+7x^2)/(9+5x)=?

x->infinity

The corresponding horizontal asymptote has equation

y=?

 

b)

lim              sqrt(7+7x^2)/(9+5x)=?

x->-infinity

The corresponding horizontal asymptote has equation

y=?

 

Answer 1

lim_x→∞ [√(7+7x²)/(9+5x)] = lim_x→∞ [√(x²)√(7/x² + 7)/(9+5x)]

 

                                                = lim_x→∞ [x√ (7/x²+7)/(x(9/x+5))]

 

                                        = lim_x→∞ [√(7/x²+7)/(9/x+5)]

 

                                        = √(0+7)/(0+5) = √(7)/5