Mathematics HL/SL/Studies Help

[Slovakov]

A function is concave up when its second derivative is positive, and concave down when second derivative is negative .

You are given a minimum and a point of inflection because there the f'(x)=0 and f''(x)=0 respectively, and they can be the boundaries of the intervals.

[dessskris]

mmm so they depend on the inflexion point?

The minimum and inflexion points are actually asked in parts a and b and when I did the latter I found out that:

when x< -1, f(x)= -ve

when x= -1, f(x)= 0

when x> -1, f(x)= +ve

So the function is concave up when x> -1, and the function is concave down when x< -1 ?

[Slovakov]

Well, yes, you're right .

That's how I see this:

f''(x) = 4e^(2x)*(x+1)

and so f''(x)>0 when x+1>0 (because 4e^(2x) is always positive)

Hence, x>-1

Edited May 7, 2011 by Slovakov

[chrypton]

This is from November 08, paper 3, sets, relations and groups, question 1)b)i):

I don't understand what they mean by:

where B,C and D are sets subsets of Z.

[Slovakov]

My textbook says that n(A) means the number of elements of a set A. I've done the same paper today, and to solve this, you first have to do part a).

[Slovakov]

I've got a problem with a paper 3 question:

"Show that the function f: R² -> R² given by f(x, y)=(3x+2y, 5x+4y)

is: a) a surjection, b) an injection

and find an expression for its inverse."

I don't know how to deal with functions with 2 variables.

The exam is tomorrow, and I came across such a weird question for the first time, so I'm quite sesperate...

Edited May 8, 2011 by Slovakov

[chrypton]

I've got a problem with a paper 3 question:

"Show that the function f: R² -> R² given by f(x, y)=(3x+2y, 5x+4y)

is: a) a surjection, b) an injection

and find an expression for its inverse."

I don't know how to deal with functions with 2 variables.

The exam is tomorrow, and I came across such a weird question for the first time, so I'm quite sesperate...

To show it's injective you use the same principle, but only with 2 variables.

So show that if:

For surjectivity, I'm not completely sure, but I'll post here once I get it.

Edited May 8, 2011 by chrypton

[adletaY]

A shopkeeper finds that the number of orders for an electrical good averages 2 per week. At the start of the trading week, i.e., on a Monday, the shopkeeper has 5 such items in stock.If and when his stock level is down to two items during the week, he orders another four items.

What is the probability he orders another four items?

I thought this would just be P(Sells 3 or More), but I was wrong about that so I'm stuck.

Thanks in advance for help!

Edited May 15, 2011 by adletaY

[dessskris]

Let's say I have a system of 3 equations:

x+2y-3z=5

3x+y+2z=4

5x+7z=5

When I try to find the rref, the last row gives me (0 0 0 2). So there is no solution.

The question is:

Describe the geometrical relationship of the 3 planes represented by this system of equations.

What should I say? Can I just say that there is no intersection of the 3 planes?

Thanks.

[nametaken]

Let's say I have a system of 3 equations:

x+2y-3z=5

3x+y+2z=4

5x+7z=5

When I try to find the rref, the last row gives me (0 0 0 2). So there is no solution.

The question is:

Describe the geometrical relationship of the 3 planes represented by this system of equations.

What should I say? Can I just say that there is no intersection of the 3 planes?

Thanks.

There are three parallel and distinct planes.

So there is no point of intersection.

There is no solution for the system of equations

[dessskris]

I also thought of saying something along those lines... but the answer in the marking scheme is:

Two planes meet in a line and the third plane is parallel to that line.

There must be something I missed here. How can we know that two planes are parallel, or a plane is parallel to a line?

[chrypton]

I also thought of saying something along those lines... but the answer in the marking scheme is:

Two planes meet in a line and the third plane is parallel to that line.

There must be something I missed here. How can we know that two planes are parallel, or a plane is parallel to a line?

You know that two lines are parallel if the direction vectors of the two can be simplified to the same vector.

If you want to know if a plane is parallell to a line, then you can take the dot product of the normal vector of the plane and the direction vector of the line, and if the dot product is 0, then you know the plane and line are parallell.

Edited May 17, 2011 by chrypton

[dessskris]

thanks! too bad I haven't learnt vectors though. can we tell from the rref only?

[chrypton]

thanks! too bad I haven't learnt vectors though. can we tell from the rref only?

Then you have nothing to worry about Vectors do take a while, but once you get it, its one of the easiest things in Math HL.

You mean row reduction? That is usually used to find out if three planes intersect at a point, line or don't intersect at all.

[Hinuku]

Hi,

I have the TI nspire with touchpad calculator. I don't know how to find a value of a function. For example, if I graph sinx and I want to find its value for x= 23213312/213131. How do I do it? In the old calculator, TI 84, I think there was something like Guess Value. Its a really good function of the calculator so it must be there! And I know I can trace but that doesn't work so well if I want to find very big or very small values.

Thanks,

Matt

[dessskris]

I hope vectors would be manageable... I've hated integration and trigo so far. don't want to add more enemies.

---

Hi,

I have the TI nspire with touchpad calculator. I don't know how to find a value of a function. For example, if I graph sinx and I want to find its value for x= 23213312/213131. How do I do it? In the old calculator, TI 84, I think there was something like Guess Value. Its a really good function of the calculator so it must be there! And I know I can trace but that doesn't work so well if I want to find very big or very small values.

Thanks,

Matt

Ok you've plotted y=sin(x) right? Click menu, 5 Trace, 1 Graph Trace, just type in the value of x straightaway (you can just put 23213312/213131) and press enter. Look at the bottom of the screen it will give you the coordinates of that point. Or if you press enter once again it will be made a point and its coordinates will appear on the screen. Let me know if it doesn't work with your calculator.

Edited May 17, 2011 by dessskris

[dessskris]

is 2arcsin(-x) = -2arcsin(x) ?

if yes, is -arccos(x) = arccos(x) ?

or is -arccos(x) = -arccos(-x) ?

I'm confused

[timtamboy63]

2arcsin(-x) = -2arcsin(x)

Yes

-arccos(x) = arccos(x)

By definition no. If arccos(x) = a, then you're asking does -a = a.

-arccos(x) = -arccos(-x)

This can be simplified to:

arccos(x) = arccos(-x),

Which is true.

You just need to remember that cos is the x value in the unit circle, and sin is the y value.

[dessskris]

You just need to remember that cos is the x value in the unit circle, and sin is the y value.

What do you mean by that? And what can you infer from that?

[chrypton]

You just need to remember that cos is the x value in the unit circle, and sin is the y value.

What do you mean by that? And what can you infer from that?

I drew a picture attempting to explain that:

Edited May 17, 2011 by chrypton