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Hi! For #2 of the AP Problems on the turn-in the table has two f(x) values for when x=5. Should the second x=5 actually be a 6? If not, is it possible to solve with [4, 6] when the value at 6 is unknown? -Claire Westerlund
ReplyDeleteYes, the last x value should be 6 and not 5. Sorry about that.
DeleteFor this problem are we allowed to draw a graph with a short explanation?
DeleteI am a little confused about infinite limits. I understand how to evaluate the limit when x approaches infinity, but I don't understand how to when x approaches negative infinity. What do we do differently to find the limit for negative infinity? -Zoe Bowers
ReplyDeleteI believe that the limits are the same for positive and negative infinity in most of the cases we talk about... It's the same process- the horizontal asymptote stretches across the whole graph! -Skyeler McQueen
DeleteThe best way is to look at the graph of the function. Exponential functions have much different behaviors as x approaches negative infinity versus positive infinity. As Skyeler pointed out, rational functions have the same end behavior if they have a horizontal asymptote.
DeleteWhat are the steps that one must go through in order to "prove" something?
ReplyDeleteexample. p.80 #48
"Prove that if f is continuous on an interval, then so is I f I." (absolute value of f)
-Sarah Mostofizdaeh
A proof is simply an irrefutable mathematical argument. So, knowing that f is continuous, what properties apply to it that we can use to show |f| is also continuous? They are listed in the text and are very "common sense".
DeleteThis may be a dumb question, but what does int mean before a function?
ReplyDelete-Rachel F
That is the notation for the greatest integer function. Kind of like abs(x) means absolute value of x. Your calculators even have this function in them.
DeleteHow would one know if f(x) is not differentiable because of a cusp rather than a corner, and vice versa?
ReplyDeleteA cusp will occur when the one sided derivatives from either side of the x-value approach infinity (vertical tangency) while a corner will occur when the one sided derivatives approach finite values, but different finite values (absolute value function).
Delete