What are budgeting approaches?

Calculus: Find the limit as x approaches 0 (e^(x) -1)/x? find the limit as x approaches 0 (x+1)^(100) - 1/x?

• Find the limit as x approaches 0 (e^(x) -1)/x? Find the limit as x approaches 0 (x+1)^(100) - 1/x

• Answer:

  Recall the formal definition of f(x) = e^x at x = 0 : lim(x-->0) (f(x) - f(x))/x = lim(x-->0) (e^x - 1)/x = e^0 = 1 for the second part (1+x)^100 --->1 as x-->0 and 1/x -->inf as x-->0 etc.