Question

Is it undefined or 5? What's the correct answer?

Answer 1

Factor the numerator and simplify.

Answer 2

x^2 +x-6=(x+3)(x-2)

so now finding limit of (x-2)(x+3)/(x-2)
you can cancel out the x-2 from both the numerator and denominator, you just need to find the limit of x+3 as x approaches 2, which would just be 5

Answer 3

L'Hopital says it's 5.

Answer 4

Factor the numerator as (x+3)(x-2) then cancel out x-2 from the numerator and denominator you'll be left out with x+3 whose limit is 2+3=5 when x tends to 2.
So the answer is 5.

Answer 5

Can you even have undefined limits? (genuine question)

Answer 6

One way to intuitively understand the concept of limits is to plug in values very very close the number in question ,when faced with an indeterminate form ; eg plugging in 2.001 , 2.0001, 2.00001 and from the other side with 1.999, 1.9999, 1.99999 , when plugged in you’ll see it approaching 5 ; although in this particular problem factoring should be the first step as it cancels out the (x-2) in the denominator

Answer 7

5, since it ends up in the indeterminate form if you plug in, you can use LHopital’s rule and take the derivative of the numerator and denominator, giving you (2x+1)/1. From there just plug in 2

Answer 8

5 is the correct answer.

Answer 9

5.

Answer 10

its 5. There are two ways!  
1. Factoring the numerator. In this case its (x+3)(x-2), then u can cancel out x-2, leaving x+3 left. Just substitute the given limit (2), 2+3 = 5.  
2. By L'Hopital's Rule, since the equation is undefined, u can get the derivative of both the numerator and denominator. Equations becomes (2x + 1)/(1) or basically just 2x +1. Substitute the 2 again, and u'll get 5. (NOTE: There are certain rules when using the L'Hopital's. It can be only be used if the equation is 0/0 or infinity/infinity. If it's not in that form, there are ways to transform which i won't discuss here.)  


HOPE THIS HELPS!