Dear Students,

We have already discussed first topic from Paper – I i.e. “Logic”. Today we are going to discuss the first topic from Paper – II i.e. “Limits”.

You have already studied few results of Limits in 11th standard.

For CET, you need to remember all the standard limits.

Apart from the standard limits you need to remember the results like

a ² – b ² = ( a – b ) ( a + b )

a ³ – b ³ = ( a – b ) ( a ² + ab + b ² )

 

and so on …

Also, you need to remember all the formulae from Trigonometry.

These are : the fundamental identities; trigonometric ratios for 2θ, 3θ, θ / 2; trigonometric ratios of allied angles; addition and subtraction formulae, factorization and defactorization formulae.


The two very important formulae which students usually don’t remember are

1 – cos 2θ = 2 sin ² θ

1 + cos 2θ = 2 cos ² θ

These two formulae are used frequently in not just limits but also in Derivatives and Integration.


While studying limits from CET point of view, you must know one result : L Hospitals Rule


The Rule is as follow

 

 

where f‘ (x) and g‘ (x) are derivatives of f (x) and  g (x) respectively.

Due to this result solving sums on limit for CET becomes very easy. However, remember that this result can be applied only if the given function is of the type

 

 

 

The rule can be applied repeatedly, consider the following example.

 

 

By L Hospitals Rule

 

Thus, while solving MCQ on limits, check whether you can apply L Hospitals Rule.

But, for few sums we can get answer faster by applying the standard methods rather than the L Hospitals Rule.

Also, for few sums even if the rule can be applied we can’t get answer easily, and we have to use the standard method only.

For example for the limit

If you try to solve it by L Hospitals Rule, it is not possible. So, we have to use the standard substitution.


You can also remember and use results like

Note that the above results and also the L Hospitals Rule cannot be used as standard results for your Board Exams.

 

 

Tags

• Maths
• MHT-CET