Question

determine the infinite limit of
lim x+2/x+3
x->-3+

Answer 1

This limit is negative infinity. Because we're evaluating the limit as x approaches -3 from the right, we know that we're dealing with values of x > -3. If x > -3, then x + 3 > 0. The expression in the denominator will approach a very small, positive number as x approaches -3 from the right. The numerator will be approaching the constant value of -1. Think about what happens when we divide a negative constant by a very small positive number. First of all, we know the answer will be negative, because we're dividing a negative and a positive. But second of all, it will be a very large and negative number, because -1 divided by (let's say, for example) 0.0001 is -10,000. As x gets closer and closer to -3 from the right, the value of this expression will be getting larger and larger in the negative direction, without bound. Therefore, the limit is negative infinity.