Need Help On Calculus

Ever since finishing my calc classes in school, I think I've done more calc on TW than at work or in school haha

 

Here we go, week 2!

Working on these two, so far only got the first two problems on number 3 and the first two on number 4.
I got to turn these in tomorrow, so any help would be great.
I'm basically reading over the lectures and hoping it makes sense before then.

 

On 3, numbers 62 and 64 do you have to find the derivative using limits or can you solve by any way you choose?

 

If it's any way you want...

62) f(x)= x^2

f'(x)= 2x

f'(-2)= 2(-2)

= -4

64) f(x)= 1/x

rewrite as x^-1

f'(x)= -x^-2

which is the same as -1/x^2

f'(-2)= -1/ (-2)^2

= -1/4

 

Ah I wish I remembered how to do this stuff...... If you ever need help also try wolfram alpha. Tends to be pretty helpful with calc.

 

62) by limit

lim f(x) f(x+h)+f(x)/ h
h--> 0

f(x)=x^2

L= [(x+H)^2 + (x^2)]/h
L= (x^2+ 2xh+h^2)/h
Cancel
= 2x+h
h=0, so f'(x)= 2x

Note: After initially writing out the limit and h approcaches stuff I abbreviated with L for the rest of the problem.

 

for 14 on page 4 you should just be able to plug and chug.

=-(1/1+1)(1+6/1)(3-1/7)
= -1

 

on 14 you could also multiply everything together first and then plug in 1 after.

 

Oh and remember that when in doubt, you can almost always make a table of values to find the limits

 

for the limits approaching infinity you divide everything in both the numerator and denominator by the highest power of x in the denominator.

not sure where i could find the pi sign on my keyboard so im just going to use "n" instead

so for 38 we have Lim as x--->-infinity(n-(2/x^2))

divide everything in the fraction by x^2

L = n - (2/x^2)/1

when you plug in negative infinity for x in 2/x^2 you get a tiiiiiiiiiiiiiny number so it is assumed as zero.

which leaves you with L= n- 0/1

you can get rid of the 0/1 which leaves Pi as your answer.

So, the Lim x-->-infinity of (n-2/x^2) = Pi.

 

Hopefully that helped

 

You guys are confusing the hell out of me. I took Algebra 2 three times. But OP, if you ever need help with History, English, or something else other than math, I could probably give you a hand.

 

Wow! I'm going to look over it all and see if I can get it.
Thanks a lot

 

Haha I'll keep that it mind, thanks!

 

I actually have the phone app, which is great. Unfortunately wolfram isn't allowed on test

 

Here's more work. I think I know what to do on 5 & 6, but I'm absolutely clueless on 7. I've attached all three. Anybody care to help?

 

Shit this all is too far gone for me, is it calc 2?

Hopefully it's fresher in someone else's mind. I'd never thought I'd say this but...

KONAAAAAAAA! HEEEEEEEEEEEEELP!

 

It's calc 1. I managed to answer every question, but my confidence isn't too high. I just need to turn in something though.

 

241? are you at Manoa?

 

Yup, I got Myers. Everyday except Tuesdays.