Integration, Definite Integrals - IB Mathematics IB maths SL

Integration, Definite Integrals - IB Mathematics IB maths SL

How can we find the real number a>1 for which the following definite integral equals to 4?




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http://www.ibmaths4u.com/viewtopic.php?f=11&t=426

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IB maths - Logarithmic equations

Logarithmic equations
How can we solve the following logarithmic equation:



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http://www.ibmaths4u.com/viewtopic.php?f=3&t=411

IB mathematics HL - Binomial Theorem

IB mathematics HL - Binomial Theorem

How can we find the coefficient of of the expansion of ?

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http://www.ibmaths4u.com/viewtopic.php?f=3&t=412

IB mathematics Higher Level - Mathematical Induction

IB mathematics Higher Level - Mathematical Induction

How can we prove by induction that is divisible by for every natural number with ?

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http://www.ibmaths4u.com/viewtopic.php?f=3&t=413

IB Maths HL - Mathematical Induction Series

IB Maths HL - Mathematical Induction Series

How can we prove by induction that for every natural number with ?

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http://www.ibmaths4u.com/viewtopic.php?f=3&t=414

IB maths HL - Mathematical Induction inequality

IB maths HL - Mathematical Induction inequality

How can we prove by induction that for every natural number with ?

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http://www.ibmaths4u.com/viewtopic.php?f=3&t=415

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 .

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