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Help with beginner college calc plz:
I can't upload pictures on my computer (it's a very old desktop) but I'll try and explain what I did. So obviously I started with graphing f(x);

(2, 1)
(-2, 1)
(0, -1)
(3, 4)
(-3, 4)

Then I drew my rectangles. The first one's width was 0 to 1.5, and the 2nd's width was 1.5 to 3 (this is where my problem came in - I will explain). My height for the 1st rectangle was 2 and the 2nd was 4. To reiterate these are right hand rectangles.

Then I did l . w so the 1st rectangle's area would be 3 and the 2nd's 12 adding up to 15.

My question though is how would you draw your two rectangles? The estimate should be from 0 to 4, but my 2nd rectangle's upper right corner only touched 3,4.

Edit: Or did I graph my parabola completely wrong?

user165349
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    What is f(x) = 1/2x^2 - 1 supposed to be? Use brackets. – The Pointer Feb 11 '21 at 16:19
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    (1/2)x^2 - 1. Does that make it a bit more clear? – user165349 Feb 11 '21 at 16:24
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    Whether it's $\frac12 x^2-1$ or $\frac1{2x^2}-1$, $f(3)$ doesn't seem to equal $4$... – Misha Lavrov Feb 11 '21 at 16:24
  • Yes that's the problem I'm having. I don't know where I went wrong on my graph. – user165349 Feb 11 '21 at 16:26
  • You'll need to use the correct value of f(3), and also should calculate f(4) since the graph has to go from x=0 to x=4. – Jaap Scherphuis Feb 11 '21 at 16:40
  • @JaapScherphuis Scherpius But wouldn't my graph still be incorrect? The parabola (at least when I drew it), went from -3 to +3. I know with RHR the upper right corner has to touch the curve, and if I went to 4 it would go over right (it wouldn't touch the curve anymore)? Oh and thanks for your help! – user165349 Feb 11 '21 at 16:47

1 Answers1

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Your graph should look like this:

enter image description here

Also note that $f(4)=7$ and $f(3)=\frac{1}{2}\cdot 9-1$.

Alicia
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