# How do you find the limit of #(4x^2)/(x-2)# as x approaches 2?

I think that it diverges giving you:

By substituting values near

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

To find the limit of (4x^2)/(x-2) as x approaches 2, we can use direct substitution. However, substituting 2 into the expression results in an undefined value, as the denominator becomes zero. Therefore, we need to simplify the expression before substituting. By factoring the numerator, we get 4x^2 = 4(x)(x). Canceling out the common factor of (x-2) in the numerator and denominator, we are left with 4x/(1). Now, we can substitute 2 into the simplified expression, which gives us 4(2)/(1) = 8. Hence, the limit of (4x^2)/(x-2) as x approaches 2 is 8.

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 #x/e^x# as x approaches infinity?
- How do you evaluate the limit of #(x^2+5x+6)/(x^2+x-2)# as #x->2#?
- How do you find the limit of #sinx/(2(x^2)-(x))# as x approaches 0?
- For what values of x, if any, does #f(x) = tan((3pi)/4-9x) # have vertical asymptotes?
- How do you find the limit of #(1 - cos^2 1) / x# as x approaches 0?

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