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as for b)
multiply and divide by \[\sqrt{x+1}+\sqrt{x}\]

that gives u 1 / √x+1+√x

when u put in infinity
it gives u 1/inf = 0

a)
dy/dx=
2xe^x3 + 3x^4e^x^3

b) him1618 already got the right answer.

was a wrong?

I guess :)

By the way, in a) if the limit approaches 5 from the left, it would be -infinity.

so ur saying it doesnt exist?

Yep.

yeah neway its a sort of hyperbola centred at 5

It has a vertical asymptote at x=5.

Question 3:
Define the min/max of \[f(x)=x^{3}-12x ^{2}+21x+25\] in [-1, infinity[

differentiate it
f'(x) = 3x^2 - 24x + 21

the roots are 7, 1

Question 4:
Define the local min/max of
\[f(x,y)=x ^{3}-y ^{3}+3xy\]

Sick how good you are :) Two more questions...

yeah go on

a) x<=0

is it right

anwar is like totatally right!

so am i man..dont demean me..lol

Why is the part x^2+2x+2 always >0?

because its determinant is negative...

Yeah. You're the one who got the answer. I was just following your foot steps :)

it is an upward parabola where the min value is greater than 0

Ah I understand :)

You deserve a medal him1618.

thnx a lot

I gave one too :)

You're welcome :)

so kind

I want to solve part b) in inequalities.

b) x is in 0 to 16

Please do I can't solve it :/

thats d ans

its damn tedious to write these eqns

Yeah, that sucks....

on d comp only..on paper it took a minute

i think i considered all the cases for 6a

2 is \[\log_{4}16 \]

But x has to be a positive number, So 0

right

Nice answer myininaya helpd me a bunch :)

here is 6b

yeah 6a is bloody tedious..nice wrk

b is right 2

Right on the spot AnwarA I'll jot that down to my notebook :)

Did anyone solve 6a, or I can take it?

yes its been solved
by myininaya

I hate you man >.<

woman* lol

OMG.. I don't hate you at all :P

lol

you can look over my work. there might be a mistake who knows

it looks good to me though

I can hardly read it :P

:(

i can rewrite it

No, It's right. I got the exact same answers.

you can also graph it in your calculator if you want to verify your answers

x=15/2 for x>=3, x=-5/2 for x<=2. No solution for 2

right!

i can write neat when i'm not trying to beat you guys to answer the questions lol

i wish in high school there was a math quiz bowl and i participated that would have been so fun

lol we should divide the questions equally. I wish I had a scanner -.-

log4 to base to is 2.

to base 2*

because 2^2=4

Mm, yes of course!
:)

Do you still have any questions, or that's it?

I think that is about it :) So quick and dirty. Thanks a million for all of you!

yes all your questions were being answered so quickly by him
hes such a meanie

no probs mate

yeah thats kind...

lol i'm kidding

dont sweat..i hate studying so much...bt i lov doing this

I think that is about it :) So quick and dirty. Thanks a million for all of you!

well thnx

Good luck in your exam on Friday :)

yeah good luck...remember me if u feel nervy..lol

Thanks, I believe I can make it :D