# What is the limit of #(x^2 + x + 4)/(x^3 - 2x^2 + 7)# as x approaches a and when does the limit exist?

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

The limit of (x^2 + x + 4)/(x^3 - 2x^2 + 7) as x approaches a is determined by evaluating the expression when x is very close to a. The limit exists if the expression approaches a specific value as x gets arbitrarily close to a. To determine if the limit exists, we need to check if the denominator becomes zero at x = a. If the denominator does not equal zero at x = a, then the limit exists.

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.

- How do you find the limit of #(xcosx)/sinx# as x approaches 2?
- How do you evaluate the limit #-r+3# as w approaches #2#?
- How do you find the limit of #(-2x^3)/(9-x^2) # as x approaches -3 from the left?
- What makes a function continuous at a point?
- Is it true that if f(x) < g(x) for all x ∈ (c-ε , c+ε ) and that lim x -> c f(x) and lim x-> c g(x) both exists that lim x->c f(x)< lim x->c g(x)?

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