SOLUTION: Hi, please help me in finding this. lim┬(x→5) ((x-5)/(x^2-5)) Which is correct? a, b, c or d? Would very much appreciate detailed workings if possible so I can better

Algebra ->  Rational-functions -> SOLUTION: Hi, please help me in finding this. lim┬(x→5) ((x-5)/(x^2-5)) Which is correct? a, b, c or d? Would very much appreciate detailed workings if possible so I can better       Log On


   

Question 991901: Hi, please help me in finding this. lim┬(x→5) ((x-5)/(x^2-5))
Which is correct? a, b, c or d? Would very much appreciate detailed workings if possible so I can better understand this question. Much Thanks.
a) 0
b) 10
c) 20
d) The limit is not defined.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the answer for this one would be 0.

the equation is (x-5) / (x^2 - 5).

when x = 5, this becomes 0 / 20 which is equal to 0.

if you said as x approaches sqrt(5), then the answer would be undefined.

that's because at x = sqrt(5), the denominator of x^2 - 5 would be equal to 0.

this can be seen on the graph.

in fact, the graph is undefined when x is equal to plus or minus sqrt(5).

$$$

the sqrt(5) is equal to 2.236 rounded to 3 decimal places.