Random Q's for exam...

[schnappy]

I've managed to get a fair idea of this binomial expansion stuff... but if I'm asked to find the coefficient of the 'x^11' term, how do i know which term this is in the expansion? TSFX appear to magically now.

[Elnino_Gerrard]

I've managed to get a fair idea of this binomial expansion stuff... but if I'm asked to find the coefficient of the 'x^11' term, how do i know which term this is in the expansion? TSFX appear to magically now.

its pretty easy.
 What i do is write the powers of all the terms---like the first is is 14,0 (o for the 3/x bit) The next one 12,1 and 12-1 is 11 so thaats it

[Whatlol]

So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?

What about no solutions :S?

for no unique solutions find when DETERMENANT = 0 .

this covers the case of both infinite and no solutions.

when you have no solutions, the two equations are parallel and will never intersect. i.e same gradient different y intercept.

for infinite, they both the same.

[akira88]

So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?

What about no solutions :S?

No solutions would also be when the determinant is 0. Then you have to make sure the lines aren't the same.

[stonecold]

So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?

What about no solutions :S?

Nah, it is:

Determinant = 0 can mean either infinite or no solutions.  You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal.

[andy456]

So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?

What about no solutions :S?

Nah, it is:

Determinant = 0 can mean either infinite or no solutions.  You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal.

So what would you do after you've found out there are unique solutions

[stonecold]

So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?

What about no solutions :S?

Nah, it is:

Determinant = 0 can mean either infinite or no solutions.  You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal.

So what would you do after you've found out there are unique solutions

Depends what the question wants.  Usually it will ask for the values which a unique solution exists or doesn't exist.

When you get given an equaution, you generally assume that it has solutions though...

[lovingit]

What is the difference between stictly increasing functions and (non-strcitly) increasing funtcions?

[3Xamz]

So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?

What about no solutions :S?

Nah, it is:

Determinant = 0 can mean either infinite or no solutions.  You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal.

So, if you sub back in and the variables cancel out and you end up with something like 2=2, does that mean no solutions?