IB mathematics HL - Graph of the Reciprocal of a Function

Reciprocal of a Function

The following guidelines are useful in order to sketch the reciprocal of a function given the graph of the original function:


Where is positive or negative then is also positive or negative respectively.

Where has zero(s) then the reciprocal function has vertical asymptote(s) and vice versa.

Where has a horizontal asymptote at y=c then the reciprocal function has also horizontal asymptote at .

Where the original function is increasing then the reciprocal function is decreasing.

Where the original function is decreasing then the reciprocal function is increasing.

If the original function has a maximum at then the reciprocal function has a minimum at .

If the original function has a minimum at then the reciprocal function has a maximum at .

If the original function has a point of inflexion at then the reciprocal function has also a point of inflexion at .

http://www.ibmaths4u.com/viewtopic.php?f=3&t=408

Application calendar for all UCAS applications

Timetable for 2013 applications

http://www.ucas.com/members-providers/undergraduate/key-dates

New!! IB Maths Revision Notes by www.IBmaths4u.com

IB Maths Revision Notes - IB Mathematics HL, SL, Studies Revision Notes by www.IBmaths4u.com

Complex Numbers for IB Mathematics HL 
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370


Mathematical Induction for IB Mathematics HL
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370


Trigonometry for IB Mathematics HL
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370

The Mathematics of Animal Behavior: An Interdisciplinary Dialogue

A very interesting article about  Mathematics of
Animal Behavior
Shandelle M. Henson and James L. Hayward

http://www.ams.org/staff/jackson/fea-henson.pdf

The Commutative Algebra

The Commutative Algebra of Singularities in Birational Geometry: Multiplier Ideals, Jets, Valuations, and Positive Characteristic Methods

Month: May 2013

Date: May 6--10

Name: The Commutative Algebra of Singularities in Birational Geometry: Multiplier Ideals, Jets, Valuations, and Positive Characteristic Methods

Location: Mathematical Sciences Research Institute, Berkeley, California.

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Description

The workshop will examine the interplay between measures of singularities coming both from characteristic p methods of commutative algebra, and invariants of singularities coming from birational algebraic geometry. There is a long history of this interaction which arises via the "reduction to characteristic p" procedure. It is only in the last few years, however, that very concrete objects from both areas, namely generalized test ideals from commutative algebra and multiplier ideals from birational geometry, have been shown to be intimately connected. This workshop will explore this connection, as well as other topics used to study singularities such as jets schemes and valuations.

Information

http://www.msri.org/web/msri/scientific/workshops/all-workshops/show/-/event/Wm9000

IB Mathematics HL– Calculus, Differentiation, Related rates, Rate of change


How can we solve the following related rates word problem?
“A 10-metres ladder is leaning against a vertical wall. The foot of the ladder slips away from the wall at the rate of 0.1 meter per minute. How fast is the top of the ladder sliding down the wall when the top is 4 meters above the ground?”
http://www.ibmaths4u.com/ib-maths-hl-rate-of-change-t258.html

The answer is at www.ibmaths4u.com

Math and Music Enthrall at MAA Distinguished Lecture

When St. Mary’s College of Maryland mathematics professor David Kung heard a public radio story about a presentation devoted to math and music, he took issue with the presentation’s title.

The seminar was called "Math and Music—Closer Than You Think," but, as Kung told a packed auditorium at the Carnegie Institution for Science on February 26, he already regarded the two disciplines as "epsilon apart."

From http://www.maa.org/dist-lecture/2013DL_SymphonicEquations.html