Prelim 2016 Maths Help Thread (1 Viewer)

[kawaiipotato]

Answer: (e^(x+1))/(x+1) + C (assuming e is a variable and not Euler's Number)

 

[InteGrand]

Answer: (e^(x+1))/(x+1) + C (assuming e is a variable and not Euler's Number)

 

[Green Yoda]

For which values of k does (2k-3)x^2+(k+1)x-1=0 has two roots.
I know how to do these questions but the answer says k>1 or k<-11
Is this wrong? as I get the delta as k^2+10k-10

 

[InteGrand]

For which values of k does (2k-3)x^2+(k+1)x-1=0 has two roots.
I know how to do these questions but the answer says k>1 or k<-11
Is this wrong? as I get the delta as k^2+10k-10

 

[Green Yoda]

OMFG...I expanded the first part as k^2+2x+2
I am retarded

 

[Paradoxica]

Just waiting for you to pounce on that...

 

[Suu]

HMm, just wondering, how would you find the derivative of a circle?

 

[InteGrand]

HMm, just wondering, how would you find the derivative of a circle?

 

[leehuan]

HMm, just wondering, how would you find the derivative of a circle?

The idea is that a derivative isn't strictly defined in terms of one variable if we're talking about implicit functions, which is what a circle is.

A circle is not actually a function because it fails the vertical line test. That's why you have to do what InteGrand did and consider two relevant semi-circles

 

[Suu]

The idea is that a derivative isn't strictly defined in terms of one variable if we're talking about implicit functions, which is what a circle is.

A circle is not actually a function because it fails the vertical line test. That's why you have to do what InteGrand did and consider two relevant semi-circles

Ahh, I see now ^^
I spent a bit too much time on the bus two days ago thinking about derivation ^^

 

[Green Yoda]

for what values of m is the following real
x^2+2mx+2(m+12)=0
I got m<=-4 or m>=6
but the answer is m<=-4 or m>6, why so?

 

[davidgoes4wce]

for what values of m is the following real
x^2+2mx+2(m+12)=0
I got m<=-4 or m>=6
but the answer is m<=-4 or m>6, why so?

Just be careful it couldn't be equal to (no need for the equal to sign)

 

[Green Yoda]

Just be careful it couldn't be equal to (no need for the equal to sign)

But isnt it Δ>=0 for real values cuz Δ=0 is still an real value?

 

[InteGrand]

The roots will be real if and only if the discriminant is non-negative (doesn't need to be strictly positive; when the discriminant is 0, the roots are real, but they're identical, i.e. double root).

 

[Green Yoda]

So why is m>6 and not m>=6?

 

[davidgoes4wce]

I was just reading off a link online

http://www.slideshare.net/swartzje/166-quadratic-formula

Not sure how reliable it is

 

[davidgoes4wce]

If the Discriminant > 0 (there are two roots)

If the Discriminant =0 (there is 1 root)

If the Discriminant <0 (there are 0 roots)

 

[InteGrand]

So why is m>6 and not m>=6?

In the absence of any further information, I'd guess it's just a typo or something.

 

[Green Yoda]

In the absence of any further information, I'd guess it's just a typo or something.

No further info was given, probs just a textbook mistake?

 

[Nailgun]

But isnt it Δ>=0 for real values cuz Δ=0 is still an real value?

This is correct

delta is only imaginary when it is less than 0

this is because in quad formula delta is square rooted

can't square root a negative number and get real answers

however you can square root 0 and postiives