# How do you evaluate the limit #(x^2-5x+4)/(x^2-2x-8)# as x approaches #4#?

Factor both the numerator and the denominator, to see what you can eliminate before substituting.

Hopefully this helps!

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

To evaluate the limit of (x^2-5x+4)/(x^2-2x-8) as x approaches 4, we substitute 4 into the expression. This gives us (4^2-5(4)+4)/(4^2-2(4)-8). Simplifying further, we have (16-20+4)/(16-8-8), which becomes 0/0. This is an indeterminate form. To evaluate the limit, we can factorize the numerator and denominator. Factoring the numerator gives us (x-4)(x-1), and factoring the denominator gives us (x-4)(x+2). Canceling out the common factor of (x-4), we are left with (x-1)/(x+2). Substituting 4 into this expression gives us (4-1)/(4+2), which simplifies to 3/6 or 1/2. Therefore, the limit of (x^2-5x+4)/(x^2-2x-8) as x approaches 4 is 1/2.

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 evaluate # [ ( ln x ) / (x^2 + x - 2 )]# as x approaches 1?
- How do you find the limit using the epsilon delta definition?
- How do you find the limit of #(x-sinx)/ (x^3)# as x approaches 0?
- How do you evaluate the limit #lim (3^x-2^x)/x# as #x->0#?
- For what values of x, if any, does #f(x) = 1/((x+8)(x-7)) # have vertical asymptotes?

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