What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?
Practice Questions
Q1
What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?
0
1
2
Infinity
Questions & Step-by-Step Solutions
What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?
Step 1: Identify the limit we want to find: lim (x -> 1) (x^2 - 1)/(x - 1).
Step 2: Substitute x = 1 into the expression. We get (1^2 - 1)/(1 - 1) = (1 - 1)/(0) = 0/0, which is an indeterminate form.
Step 3: Since we have an indeterminate form, we can use L'Hôpital's Rule. This rule states that if we have 0/0 or ∞/∞, we can take the derivative of the top and the derivative of the bottom.
Step 4: Find the derivative of the numerator (x^2 - 1). The derivative is 2x.
Step 5: Find the derivative of the denominator (x - 1). The derivative is 1.
Step 6: Now we can rewrite the limit using the derivatives: lim (x -> 1) (2x)/(1).
Step 7: Substitute x = 1 into the new expression: (2*1)/(1) = 2/1 = 2.
Step 8: Therefore, the limit of (x^2 - 1)/(x - 1) as x approaches 1 is 2.
