But that's wrong. lim of x-> implies that 8 is being approached from both side which would result in two different results, one side resulting in infinity and the other resulting in negative infinity. As it is written, the answer would be "does not exist."
Also, the bottom is wrong because sideways 5 isn't a number.
Not to burst anyones bubble, but it does require small ammounts of math to build a wall out of bricks..theres a certain pattern u must keep for the wall not to simply fallover.
You're confusion is not suprising, ignore the comments below they're wrong as well, when you divide something by increasingly smaller numbers the numbers you start to get get a lot bigger for example if you divide 1/10 you get 0.1 if you divide by 1/1 you get 1 if you divide by 1/0.1 you get 10 if you divide by 1/0.00000000 you start to tend towards an infinityly large number and thats what this means of course it's impossible to divide by zero but as you approach the limits 1/0 tends to infinity
When you graph 1/(x-8), you'll get an asymptote with the limit approaching from the left side approaching negative infinity, while the limit approaching from the right side will approach infinity. However, the first equation is wrong since when you take the limit, you must look at both sides, thus the limit doesn't exist.
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The answer to both of these limits is 'undefined', not infinite. You cannot divide by zero ever
seriously...just from observation of the previous expression and no knowledge of mathematics you can work out that that's infinity limits of the 1st one is x --> 8 and that equals infinity limits of the other one is x --> 5 ...that equals infinity as well?
It's calculus. You're finding the limit of the function when X approaches a specific number, in this case 5 or 8, so you would sub that number in. Which I now realize would be undefined, hence the need to find the limit. My bad.