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

Apply L'Hopital's:

Simplifying:

Now evaluating the limit:

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

To find the limit of (x^2 - sqrt(x))/(sqrt(x) - 1) as x approaches 1, we can use algebraic manipulation and the concept of limits.

First, we notice that the expression is undefined when the denominator becomes zero. Therefore, we need to determine if the limit exists by evaluating the expression as x approaches 1.

To simplify the expression, we can multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt(x) + 1. This will help us eliminate the square root in the denominator.

After multiplying, we get (x^2 - sqrt(x))/(sqrt(x) - 1) * (sqrt(x) + 1)/(sqrt(x) + 1).

Simplifying further, we have (x^2 - sqrt(x))(sqrt(x) + 1)/(x - 1).

Now, we can cancel out the common factor of (x - 1) in the numerator and denominator.

The expression becomes (sqrt(x) + 1)(x + sqrt(x))/(x - 1).

As x approaches 1, we can substitute it into the expression to find the limit.

Plugging in x = 1, we get (sqrt(1) + 1)(1 + sqrt(1))/(1 - 1).

Simplifying, we have (1 + 1)(1 + 1)/(1 - 1) = 4/0.

Since the denominator is zero, the limit does not exist.

Therefore, the limit of (x^2 - sqrt(x))/(sqrt(x) - 1) as x approaches 1 is undefined.

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

- How do you use the Squeeze Theorem to find #lim(x-1)sin(pi/x-1) # as x approaches one?
- For what values of x, if any, does #f(x) = 1/((2x+3)(x-6) # have vertical asymptotes?
- How do you find #lim_(x->0^-)cosx/x#?
- What does continuous at a point mean?
- How do you find #lim t(sqrt(t+1)-sqrtt)# as #t->oo#?

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