Answer to Question #1954 in Calculus for Vigi

Question

Evaluate the limit. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)

limit x->1( (5x/x-1) -(5/ln(x))

Answer 1

limit_x->1( (5x/x-1) -(5/ln(x)) = limit_x->1((5xlnx - 5x+5)/(x-1)lnx)
= limit_x->1(5xlnx - 5x+5)'/((x-1)lnx)' = limit_x->1(5 + 5lnx - 5)'/(1-1/x +lnx)' =
= limit_x->1(5/x) / ((x-1)/x²) = 5/0 = ∞