# How do you find the limit of #f(x) = (x^2 - 1) / ( x + 1) ^2# as x approaches -1?

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

To find the limit of f(x) = (x^2 - 1) / (x + 1)^2 as x approaches -1, we can substitute -1 into the function and simplify.

Substituting -1 into the function, we get f(-1) = (-1^2 - 1) / (-1 + 1)^2 = 0/0.

Since we have an indeterminate form of 0/0, we can apply L'Hôpital's rule.

Differentiating the numerator and denominator separately, we get f'(-1) = (2x) / (2(x + 1)).

Substituting -1 into the derivative, we get f'(-1) = (2(-1)) / (2(-1 + 1)) = -2/0.

Again, we have an indeterminate form of -2/0, so we can apply L'Hôpital's rule once more.

Differentiating the numerator and denominator again, we get f''(-1) = 2 / 2 = 1.

Since the derivative is now a constant, we can conclude that the limit of f(x) as x approaches -1 is 1.

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

- How do you prove that the limit of #sqrtx = 3# as x approaches 9 using the epsilon delta proof?
- What is the limit of #ln(x) / sqrtx # as x approaches #oo#?
- What is the limit of #(2+3sinx)/(x^3 +1)# as x approaches 0?
- How do you find the limit of #[1+(a/x)]^(bx)# as x approaches infinity using l'hospital's rule?
- How do you find the limit of # arctan(x) # as x approaches infinity?

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