Indeterminate Forms

Solved Problems

Solution.

Change the variable: or Then as We have

Convert the last expression using the reduction formula As a result we find the limit of the function:

Solution.

If then

Thus, we deal here with an indeterminate form of type Multiply this expression (both the numerator and the denominator) by the corresponding conjugate expression.

By using the product and the sum rules for limits, we obtain

Solution.

To calculate this limit we rationalize the numerator and denominator multiplying them by the corresponding conjugate expressions:

Solution.

We divide both the numerator and denominator by $$ (the highest power of the fraction):

Solution.

Let $$ Then $$ as $$ Hence,

Solution.

This function is defined only for $$ Multiply and divide it by the conjugate expression $$ So, we get

Both the numerator and denominator now approach $$ as $$ Hence, we divide numerator and denominator by $$ the highest power of $$ in the denominator. Then