# How do you evaluate the limit #-(t-2)/(t^2-4)# as t approaches #2#?

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

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

To evaluate the limit -(t-2)/(t^2-4) as t approaches 2, we can substitute the value of t into the expression. By substituting t=2, we get -(2-2)/(2^2-4). Simplifying this expression further, we have 0/0. This is an indeterminate form. To evaluate this limit, we can use algebraic manipulation or L'Hôpital's rule. Applying L'Hôpital's rule, we differentiate the numerator and denominator separately. The derivative of -(t-2) is -1, and the derivative of t^2-4 is 2t. Evaluating these derivatives at t=2, we get -1/4. Therefore, the limit of -(t-2)/(t^2-4) as t approaches 2 is -1/4.

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

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.

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.

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.

- What is the limit of #(2x^2-18) / (x+3)# as x approaches -3?
- Why is it impossible to have #lim_(x->0) f(x)# and #lim_(f(x)->0)f(x)# simultaneously exist for any of these graphs?
- How do you find the Limit of #ln(n)/ (ln(n))^2# as n approaches infinity?
- How do you find the limit of #f(x) = (x^2 - 1) / ( x + 1) ^2# as x approaches -1?
- How do you determine the limit of #sqrt(x-4)/(3x+5)# as x approaches negative infinity?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7