Hi I was wondering if someone could help me with this limit problem:
Find the lim x->a-, lim x->a+ and lim x->a
for the f(x)=(x^2-16)/(squareroot(x^2-8x+16)) a=4
I've tried to simplify the problem but after that i dont know wut to do =(
This is wut I've done:
y=(x^2-16)/(squareroot(x-4)^2)
y=(x^2-16)/abs(x-4)
any help would be appreciated.
The numerator is a difference of squares, so you should be able to factor it:
Now, when you take the limit, notice that is always negative when (which will be the case for the left-handed limit) and nonnegative when (which will be the case for the right-handed limit). So, get rid of the absolute value bars (negating when appropriate) and simplify.
thanks for ur help in the previous question. i was also wondering if the absolute value function was in the numerator, wut sign would i need to take for the lim->a-, lim ->a+?
Example:
f(x)=abs(x^2+5x+6)/(x^2-9)
i did the same thing as u guys hv instructed me for the other question by taking a negative value of the absolute value of the numerator wen lim->a- and positive wen lim->a+. then i was able to simplify. i was able to get a number for limits from the left and from the right. but wen i graph the function on my calculator i see that the answer is supposed to be negative infinity for the left and positive infinity for the right. im a bit confused
Now, the absolute value will depend on the values that is taking. As , is positive or negative? What about and ? How about as ? This will all, of course, depend on the value of .
When the expression is positive, you can remove the absolute bars, and when it is negative you can remove the bars as long as you negate the expression.