Home > Calculus > Determining Limits Algebraically

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

Answer 1

Paisley Johnson

#5#

#lim_(x->infty)(5+1/x)/(1+2/x)=(5+0)/(1+0) = 5/1 = 5#

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

Answer 2

Paisley Johnson

#5#

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

#"=lim_(xtooo)(5+1/x)/(1+2/x)#

#=(5+0)/(1+0)=5#

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

Answer 3

Evelyn Agard

To find the limit of (5+x^-1)/(1+2x^-1) as x approaches infinity, we can use the concept of limits.

First, we simplify the expression by multiplying both the numerator and denominator by x to get (5x + 1)/(x + 2x^2).

Next, as x approaches infinity, the terms with lower powers of x become negligible compared to the highest power term. Therefore, we can ignore the 1 in the numerator and the x in the denominator.

This simplifies the expression to 5x/x^2, which further simplifies to 5/x.

Finally, as x approaches infinity, the value of 5/x approaches 0.

Therefore, the limit of (5+x^-1)/(1+2x^-1) as x approaches infinity is 0.

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.

How do you find the limit #(5+x^-1)/(1+2x^-1)# as #x-&gt;oo#?

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