Limits

1. Concept Overview In the study of Limits, an indeterminate form arises when direct substitution of the limiting value into…

1. Concept Overview In mathematics, especially in calculus, the idea of a limit helps us understand the behavior of a

1. Concept Overview While evaluating the value of a function at a given point, we do not always need to

1. Concept Overview A limit is said to be in Zero by Zero form when: [\lim_{x \to a} \dfrac{f(x)}{g(x)}] and

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

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