4 unit questions (1 Viewer)

[forstudents]

Hey guys, just wanted to ask the questions below any help would be appreciated thank you

 

[Riviet]

See if you can upload it (go to "manage attachments" in the message options).

edit: nice job loading them up.

edit 2: you wanted help with just the circled ones or all of them?

 

[forstudents]

ok done got it fixed

 

[haque]

i've done all of em, but everytime i try and upload it says error with the server can't be connected or something. i'l try again tomorro

 

[little master]

for second link: IN=integral sign

<b> u^2= e^x +1 u= sqrt(e^x +1) </B>

Integral of e^2x/sqrt(e^x+1)*dx
du/dx= 1/2e^x (e^x +1)-1/2
IN (u^2-1)^2 / sqrt(u^2-1+1)*dx
IN {(u^2-1)^2 / u} * {2*(e^x+1)^1/2}du/e^x
2 IN (u^2-1)^2 *u du/ {u* (u^2-1)} since e^x=u^2 -1

2IN {u^2-1}du

2[u^3/3 - u]

2[{(e^x +1)^3/2} / 3 - sqrt(e^x +1)] + C

i think thats it... if u find find any mistake please post it
hope u can understand it

 

[haque]

that's right. here's the soluton for the locus question M

M: a/2(cosa +cosb), a/2(sina+sinb)
relationship from diagram b=90+a

for M
x=a/2(cosa +cosb)
2x/a=cosa-sina (cos(180-90-a))
similarly
2y/a=(sina+sinb)
=sina+cosa
squaring and adding these two equations gives on simplification
x^2 +y^2=a^2/2

 

[Riviet]

(d) Use long division OR manipulation (see below):

(y⁵ - 7y² + 8)/(y³ - 8) = {y²(y³ - 8) + y² + 8}/(y³-8)
= y² + (y² + 8)/{(y-2)(y² + 2y + 4)}

Use partial fractions on the second bit.

edit: see vafa's solution.

 

[Riviet]

For the polynomials question:

(ii) Let the roots be a, b and c.
Consider 3x³ + 4x² - 2x -1 = 0
Rearranging gives x³ = (1 + 2x - 4x²)/3 (1)
Substituting a, b and c into (1) and summing them up:
a³ + b³ + c³ = {3 + 2(a + b + c) - 4(a² + b² + c²)}/3
Use part (i) to finish simplifying.

 

[vafa]

Here is the answere to all the questions. this post contains the first 5 pages:

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[vafa]

And this is the last page.

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