Find the limit

[Baron]

Evaluate the limit as x approaches 10- of ln(100-x^2)

Nevermind, I understand the answer. If someone with godly powers could delete or lock this thread, I would greatly appreciate it.

 

[tkhunny]

Evaluate the limit as x approaches 10- of ln(100-x^2)

evaluate by plugging in 10,

Very bad. Why would you try to substitute without first determining 1) Is the value in the Domain, and 2) Is it continuous there?

Seriously, never do that.

I can't use L' Hospital's rule because there is no way to make this into infinity/infinity or 0/0.

Very good, but you can just say "indeterminate form" This has a proper technical meaning without providing the examples.

By graphing, I know the answer is -infinity but how do you get the answer without graphing?

I am often astounded at how quickly algebra fades from the mind. Calculus is not a rest from algebra, it is a proving ground for the algebra you should have learned.

Try factoring the difference of squares that is the logarithm's argument.

 

[raghvendrasingh]

If you check the domain of the function f(x)=log(100-x^2) , it is x belongs to (-10,10) now if you see the graph of f(x) ,you can see that limit does not exist when x approaches to 10 .