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Class 11 Math Ch-12: Limits and Derivatives Notes
Class 11 Maths Chapter 12 Limits and Derivatives introduces the intuitive concept of limits of functions, standard limit formulas, and the definition and basic rules of differentiation.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What does it mean for the limit of a function f(x) to exist at a point x = a?
Answer: The limit of f(x) as x approaches a exists if the left-hand limit (as x approaches a from values less than a) and the right-hand limit (as x approaches a from values greater than a) both exist and are equal to each other; this common value is then called the limit of f(x) at x = a.
Q2: State the standard limit formula for lim(x→0) (sinx / x).
Answer: The standard limit is lim(x→0) (sinx / x) = 1, a fundamental result frequently used in evaluating other trigonometric limits.
Q3: What is the standard algebraic limit formula lim(x→a) [(x^n − a^n)/(x − a)]?
Answer: The standard limit formula is lim(x→a) [(x^n − a^n)/(x − a)] = n·a^(n−1), which is widely used to evaluate limits of the indeterminate form 0/0 involving powers of x.
Q4: How is the derivative of a function f(x) defined using limits?
Answer: The derivative of a function f(x) at a point x is defined as f'(x) = lim(h→0) [f(x+h) − f(x)] / h, provided this limit exists, and it represents the instantaneous rate of change of the function at that point.
Q5: What is the derivative of xⁿ with respect to x?
Answer: The derivative of xⁿ with respect to x is given by the power rule: d/dx(xⁿ) = n·x^(n−1).
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