Question

lim x^2-x+6/ x-2
x->2

Answer 1

3

Answer 2

I have to evaluate it.

Answer 3

substitute value of x as 2 in equation

Answer 4

the answer is 5, but i don't know how they get it.

Answer 5

i did that

Answer 6

We can't substitute 2 into the equation because the denominator would be zero. Are you sure about your signs? Because x^2+x-6/x-2 readily factors into:
(x-2)(x+3)/(x-2) = (x+3)

Substituting x=2 you get (2+3) = 5

Answer 7

Your book has a typo because \[\lim_{x \rightarrow 2} x ^{2}-x+6/x-2\] doesn't exist. The line x=2 is actually a vertical asymptote of this function. The function approaches +infinity as x approaches 2 from the right and -infinity as x approaches 2 from the left. There are a number of ways to see this. Try factoring this into:\[x^2-x+6/x-2 = (x-2)(x-3)/(x-2) + 4x/(x-2)\]
(if you're not sure how I got this try expanding it and you'll see I haven't changed the value of this function). This simplifies to:\[x-3 + (4x/x-2)\] This can be brokendown even further if you want:\[x-3+[4/(1-(2/x))]\]Clearly we are going to get a vertical asymptote due to the term on the right.