Home > Calculus > Determining Limits Algebraically

How do you evaluate the limit #(x+5)/(2x^2+1)# as x approaches #oo#?

Answer 1

Emily Ammerman

Zero

Cross out the #5# and the #1#, then cancel the #x#.

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

Answer 2

Ezekiel Alexander

To evaluate the limit of (x+5)/(2x^2+1) as x approaches infinity, we can use the concept of limits. By dividing every term in the expression by x^2, we get (1/x + 5/x^2)/(2 + 1/x^2). As x approaches infinity, 1/x and 5/x^2 both approach zero. Thus, the expression simplifies to 0/2, which equals zero. Therefore, the limit of (x+5)/(2x^2+1) as x approaches infinity is zero.

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.