How do you find the limit of # (x^3 - x) / (x -1)# as x approaches 1?
And you can see from Wolfram Alpha that it is indeed correct.
By signing up, you agree to our Terms of Service and Privacy Policy
To find the limit of (x^3 - x) / (x - 1) as x approaches 1, we can simplify the expression by factoring the numerator. Factoring x^3 - x gives us x(x^2 - 1), which further simplifies to x(x - 1)(x + 1). Canceling out the common factor of (x - 1) in the numerator and denominator, we are left with x(x + 1). Now, substituting x = 1 into the simplified expression, we get 1(1 + 1) = 2. Therefore, the limit of (x^3 - x) / (x - 1) as x approaches 1 is equal to 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.
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 #lim (3^(x+1)-2^(x+4))/(3^(x-2)+2^(x-1)+6)# as #x->oo#?
- How do you use the definition of continuous to prove that f is continuous at 2 given #f(x) = x^2 -3x +5#?
- Evaluate the limit by using a change of variable?
- How do you find the limit of #(1+3/x)^(2x)# as x approaches negative infinity?
- How do you find the limit of # (8x^2)/(4x^2-3x-1)# 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