Maths in focus (2 Viewers)

[Aysce]

Personally, I only use MIF when I learn a new concept to test my basic knowledge and move on to Cambridge and Fitzpatrick where the questions increase in difficulty.

 

[iBibah]

Well Cambridge does have the set of questions before development which are just as easy as MiF, but yes I would agree it can be good if you want to test basics (stick to Cambridge )

 

[deb54]

The Maths in Focus chapter on limits is wrong. Check the solutions, she has graphs that cross asymptotes! Crazy.

 

[asianese]

Graphs can cross asymptotes - just not at extremities...

 

[Carrotsticks]

Graphs can cross asymptotes - just not at extremities...

This. Just because there's an asymptote, doesn't necessarily mean we can't cross it. It just means that EVENTUALLY the curve has to approach it.]

Typical example:



The asymptote is the X axis (since as x -> plus/minus infinity, y-> 0), but there is most certainly an x intercept at the origin.

 

[such_such]

The Maths in Focus chapter on limits is wrong. Check the solutions, she has graphs that cross asymptotes! Crazy.

Not the sketching, rather questions that involve finding the limit is incorrect.

 

[soloooooo]

This. Just because there's an asymptote, doesn't necessarily mean we can't cross it. It just means that EVENTUALLY the curve has to approach it.]

Typical example:



The asymptote is the X axis (since as x -> plus/minus infinity, y-> 0), but there is most certainly an x intercept at the origin.

What? Asymptotes cannot be crossed as n increases towards infinity.

 

[Carrotsticks]

What? Asymptotes cannot be crossed as n increases towards infinity.

I presume you mean 'as x approaches infinity', and yes they can. Refer to my above example. Here is the graph:

Like I said, as x -> infinity and x -> -infinity, the curve approaches 0.

However this doesn't necessarily mean that the asymptote is applicable everywhere, because the curve is very well-defined at the origin.