How do you evaluate the limit #(x^4+3x^3-x^2+x+4)/(x+1)# as x approaches #-1#?
2 Answers
Factor and simplify the ratio.
Explanation:
Because
Use division or trial and error to get
So,
# = lim_(xrarr-1)(x^3+2x^2-3x+4) = -1+2+3+4 = 8#
Use L'Hôpital's rule
Explanation:
Because the expression becomes an indeterminate form, specifically
The derivative of the denominator is 1, therefore, we do not need to write it into the resulting expression.
The derivative of the numerator is:
L'Hôpital's rule stipulates that the limit of the original expression is the same.