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Hey, this time I can't get the answer provided in the solutions. The question is: Calculate the values of p, q, r, s in order that 2x^3 +4x^2 + 5x + 6 and p(x-1)^3 + q(x-1)^2 + r(x-1) + s specify the same polynomial. The answer is: p=2, q=10, r=19, s=17 I have different...

Yay, thanks! :)

Can someone please help me with the following Polynomials questions? Thank you very much! Q1 If x^(3) +2x^(2)y - xy^(2) - 2y^(3) and x^(3) -7xy^(2) - 6y^(3) have (x+2y) as a factor, simplify: x^(3) +2x^(2)y - xy^(2) - 2y^(3) __________________________ x^(3) -7xy^(2) - 6y^(3)...

(Thanks for replying!) For Q2 I did what you said and I got: In(1/e + 1) - In2 but the answer is 1 - In2. How does In(1/e + 1) = 1? Or did I do something wrong?

Can someone please help me with the following questions? 1. Integrate [ x^2 . e^(2x^2) - 1 ] / x 2. Integrate [ 1 / (x+1) ] within the boundaries e^(-1) and 1 Thank you! (I hope the questions make sense...)

Oh, ok. Thanks. I'll give it a try.

tommykins: I can sketch y = (1+x)^(1/2) but I don't know how to sketch the reciprocal (in fact, I don't know how to sketch the reciprocal of any function TT). gurmies: Thanks! I also realised the answer I typed out is missing pie.

Yes, I'm interested! Can you pm me?

I would really appreciate help with these two problems. Thanks! 1) The region bounded by the curve y = x^(1/2) - 1, the lines x=2, x=3, and the x-axis, is rotated about the x-axis. Find the volume of the solid of revolution so formed. Answer: [ 7/2 - 4.3^(1/2) +(8/3).2^(1.2) ] units^3...

Templar: I haven't learnt substitution yet so I don't know how you got the new limits. Thank you for answering though. Timothy.Siu: Man, that was very straightforward. Thank you for pointing it out for me - *feels stupid*.

Find the integral, between 0 and In2, of: e^x / ( e^x + 1 ) .dx (Does that make sense?) The answer is: In(3/2) Thanks in advance!

Wow. Thank you.

Oh, I get it. Thank you!

I'm sorry. How did you get this?

Find the equation of the tangent to the curve y = e^x which passes through the origin. Ans: y = ex. I can't get the answer. :(

A window frame has the shape of a rectangle surmounted by a semicircle. The perimeter of the frame is constant. Show that, for a maximum area, the height of the rectangle is equal to the radius of the semicircle. Can someone do the above question? Thanks in advance!