I know the first question its the heights with the widths all together to finding an total decimal approximation
like another question I had was
5 / (5/2) / (5/3) / (5/4) = 1.0417 = 10.417
but the Pi is throwing me off

The second question im clueless
help would be gladly appreciated, could donate whatever I have of FG lol
Thanks

2a)does not exist, because at no place on that graph where x = -2
2b)does not exist, because while the limit approaches a y value from the left and from the right, it does not approach the same y value from the left and the right, therefore it does not exist.
2c)exists, there is a value for y that corresponds to x=0
2d)does not exist, see 2b
2e)exists, see 2c
2f)exists, y approaches the same value from both left and right, so it exists.

This post was edited by Azrad on Sep 8 2013 06:11pm

1)
Just calculate the area of each green rectangle, then sum them up.

all of the width's for the first problem are pi/4, the heights are gotten by evaluating the function at each x values (x = pi/4, x=pi/2, x=3pi/4)

so the height of the first rectangle is sin(pi/4), and its width is pi/4, so its area is:
A= L * W = Sin(pi/4) * pi/4 = sqrt(2)*(1/2) * pi/4 = sqrt(2)*pi*(1/8)

Do this for all 3 and sum them up and you will get a decent approximation for the area under the curve.

This post was edited by Azrad on Sep 8 2013 06:21pm

Ah! Thank you very much! but when looking at my questions I accidentally cropped out two extra

you try them (post your answers here if you don't want to waste an "attempt" on submitting them). Here is some hints

g) is there a point on the graph that corresponds to x = 4?

h) when you follow the curves from both directions towards x = 4, are they converging on the same locations/value?

g. yes, so it would exist because it corresponds with 4

h. yes, so it would exist because they are coming together?

/e so how would i answer those that exist? just enter the digit that they either correspond to or converge to?

This post was edited by FiestaBeast on Sep 8 2013 06:27pm

Yeah that is right. The limit for h is +∞ (have fun typing that in).

Well a strict interpretation of the instructions would suggest you leave the ones that exist blank, and write DNE in the ones that do not exist. However, I doubt this is what they really want. I'd try putting in the value of the function (or the limit) in the ones that exist. And make sure to complain about the shitty wording of the question!

This post was edited by Azrad on Sep 8 2013 06:39pm

for this, the limit would not exist since the points are together correct?

heh a tricky one.... see at you approach x =1 from both sides... the y value gets closer and closer to 2... so the limit does exist!

remember.... when given a function like f(2), we only care what the value is at x=2 and we don't give a shit about anything else....

when given a expression like the limit as x -> 2 of f(x), now we don't give a shit what happens at x=2, but instead we care about what happens NEAR the area where x =2 (on both sides)

of course the above is not the formal definitions^^^ but hopefully will give you a better feeling for it...

This post was edited by Azrad on Sep 8 2013 06:52pm