Author name: Kumar Rohan

Limits of the Form [\lim_{x→0} \dfrac{a^{x} – 1}{x}] 1. Concept Overview (Very Important for Exams) When a function involves an…

Standard Results Used (Repeated Every Time)  [\lim_{x→0} \dfrac{a^{x} – 1}{x} = \log_{e} a]  [\lim_{x→0} \dfrac{\sin x}{x} = 1] Practice Questions

Exponential Limits – Standard Results Introduction In the chapter Limits, a very important category is Exponential Limits, where the base

Practice Questions with Step-by-Step Solutions Exponential Limits of the Form [\lim_{x \to \infty} (1 + \dfrac{a}{x})^x] Question 1. Evaluate [\lim_{x

Practice Questions with Step-by-Step Solutions Question 1. Evaluate [\lim_{x \to 0} (1 + \sin x)^{\dfrac{1}{x}}] Step-by-Step Solution: Step 1: Identify

Practice Questions with Step-by-Step Solutions Exponential Limits of the Form [\lim_{x \to 0} \left(\dfrac{1 + ax^2}{1 + bx^2}\right)^{\dfrac{1}{x^2}}] Standard Result

1. Concept Overview: What Are Logarithmic Limits? A logarithmic limit is a limit in which the given expression involves a

1. Concept Overview: What Is L’Hospital’s Rule? L’Hospital’s Rule is a method used to evaluate limits of the form: [\dfrac{0}{0}]

Practice Questions with Step-by-Step Solutions Question 1. Evaluate [\lim_{x \to 1} \dfrac{x^2 – 1}{x – 1}] Step-by-Step Solution: Step 1:

1. Concept Overview The rationalisation method is used to solve limits when square roots cause the indeterminate form (0/0). It