Q.0 - Calculus

Question

Read the section and make your own summary of the material.

Step-by-Step Solution

Answer

Suppose f and g are differentiable functions on some punctured interval around x = c on which g(x) is nonzero. If $\underset{x\to c}{lim}\frac{f\left(x\right)}{g\left(x\right)}$ is of the indeterminate form $\frac{0}{0} or \frac{\infty }{\infty }$ then,

$\underset{x\to c}{lim}\frac{f\left(x\right)}{g\left(x\right)}=\underset{x\to c}{lim}\frac{f\text{'}\left(x\right)}{g\text{'}\left(x\right)}$.

The method of relating the Limit of a Function to the Limit of Its Logarithm has been learnt and the problems involving these rule have been worked out.

Step 1. Given Information.

The information in the book.

Step 2. L'Hopital Rule.

Suppose f and g are differentiable functions on some punctured interval around x = c on which g(x) is nonzero. If $\underset{x\to c}{lim}\frac{f\left(x\right)}{g\left(x\right)}$ is of the indeterminate form $\frac{0}{0} or \frac{\infty }{\infty }$ then,

$\underset{x\to c}{lim}\frac{f\left(x\right)}{g\left(x\right)}=\underset{x\to c}{lim}\frac{f\text{'}\left(x\right)}{g\text{'}\left(x\right)}$

Step 3. Using logarithms for indeterminate forms.

The method of relating the Limit of a Function to the Limit of Its Logarithm has been learnt and the problems involving these rule have been worked out.