Strategies for finding Limits

Limits

Strategies for finding Limits

1 If this does not work, try direct substitution firstly.

2 If the function is in fractional expression, The limits can often be evaluated by dividing out common factors.

3 If the function involves radicals, limits can be evaluated by rationalizing the numerator or denominator.

4 Using a graph or table is helpful to find the limits.


Problem.


1 lim_(x->0) x^2-3+5/2x+1 = ?

2 lim_(x->1) x-1 /√(x)-1 = ?


























Answer

(Click on the picture to see it bigger and more accurately.)

First problem can solve by trying to direct substitution (This method is available for most problems of this type)

Second problem can solve by rationalizing (application (A+B)(A−B)=A^2−B^2 )