Q. 96 - Calculus

Question

Use algebra, limit rules, and the continuity of ln x on $(0,\infty )$ to prove that every logarithmic function of the form $f\left(x\right)={\log }_b\left(x\right)$ is continuous on $(0,\infty )$.

Step-by-Step Solution

Answer

df

Step 1. Given Information.

Consider the given question,

Step 2: Attempt direct substitution

Try substituting the value the variable approaches directly into the expression.

Step 3: Handle indeterminate forms

If direct substitution gives an indeterminate form, apply L'Hopital's Rule, algebraic manipulation, or other techniques.

Step 4: Evaluate the limit

Compute the final value of the limit.

Step 5: State the conclusion

Express the final answer.