How do you evaluate the limit #sqrt(x-1)/(x-4)# as x approaches #3#?

Answer 1

#- sqrt(2)#

We have: #lim_(x -> 3) (sqrt(x - 1)) / (x - 4)#
This limit can be evaluated by substituting #x# with #3#:
#= (sqrt((3) - 1)) / ((3) - 4)#
#= (sqrt(2)) / (- 1)#
#= - sqrt(2)#
Sign up to view the whole answer

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

Sign up with email
Answer 2

To evaluate the limit of sqrt(x-1)/(x-4) as x approaches 3, we can substitute the value of x into the expression. However, this would result in an undefined expression since the denominator would be zero. To overcome this, we can simplify the expression by multiplying both the numerator and denominator by the conjugate of the numerator, which is sqrt(x-1) + 2. This simplifies the expression to (sqrt(x-1)(sqrt(x-1) + 2))/(x-4). Now, substituting x = 3 into the simplified expression, we get (sqrt(3-1)(sqrt(3-1) + 2))/(3-4), which simplifies to (sqrt(2)(sqrt(2) + 2))/(-1). Further simplification gives (-2(sqrt(2) + 2))/(-1), which equals 2(sqrt(2) + 2). Therefore, the limit of sqrt(x-1)/(x-4) as x approaches 3 is 2(sqrt(2) + 2).

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7