Home > Calculus > Determining Limits Algebraically

How do you find the limit of #((x/(x+1))((2x+5)/(x^2+x))# as x approaches #-2^+#?

Answer 1

Ezekiel Alexander

Neither denominator is #0# at #-2#, so use substitution.

#lim_(xrarr-2^+)((x/(x+1))((2x+5)/(x^2+x))) = (((-2)/((-2)+1))((2(-2)+5)/((-2)^2+(-2)))) = (2)(1/2) = 1#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emily Ammerman

To find the limit of the given expression as x approaches -2^+, we substitute -2 into the expression and simplify:

((x/(x+1))((2x+5)/(x^2+x))) = ((-2/(-2+1))((2(-2)+5)/((-2)^2+(-2)))) = ((-2/(-1))((-4+5)/(4-2))) = ((-2/(-1))(1/2)) = 2

Therefore, the limit of the expression as x approaches -2^+ is 2.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.