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

it indeterminate so we can simplify a bit using L'Hopital's Rule

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

To determine the limit of (x^2-2x)/(x^2-4x+4) as x approaches 2-, we can substitute the value 2 into the expression and simplify. By doing so, we get (2^2-2(2))/(2^2-4(2)+4), which simplifies to (4-4)/(4-8+4). Further simplification gives 0/0. This indicates that the expression is indeterminate at x=2-. To find the limit, we can factor the numerator and denominator. Factoring the numerator gives (x(x-2)), and factoring the denominator gives (x-2)(x-2). Canceling out the common factor (x-2), we are left with x/(x-2). Now, substituting 2 into this simplified expression gives 2/(2-2), which simplifies to 2/0. This is still an indeterminate form. To resolve this, we can use algebraic manipulation or L'Hôpital's rule. Applying L'Hôpital's rule, we differentiate the numerator and denominator separately. The derivative of x is 1, and the derivative of (x-2) is 1. Evaluating the limit of the derivatives as x approaches 2- gives 1/1, which equals 1. Therefore, the limit of (x^2-2x)/(x^2-4x+4) as x approaches 2- is 1.

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.

- How do you find the limit of # (2^x-3^-x)/(2^x+3^-x)# as x approaches infinity?
- F(x) = (x cosx + 3 tanx)/ (x² + sinx), For x≠0 f(x) = 4, for x=0 At x=0 is such that? (a) it is continous (b) it has irremovable discontinuity (c) it has removable discontinuity (d) lim f(x) = 3 x->0
- How do you determine the limit of #(pi/2)-(x)/(cos(x))# as x approaches pi/2?
- Evaluate the limit? : # lim_(x rarr oo)(3x+1)/(|x|+2) #
- How do you evaluate the limit #(3x^4-x^2+5)/(10-2x^4)# as x approaches #oo#?

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