Class 11 Mathematics — Chapter 12: LIMITS AND DERIVATIVES

What you'll learn

• ▸Intuitive Idea of Derivatives
• ▸Geometric Interpretation of a Derivative
• ▸Concept of a Limit
• ▸Left-Hand and Right-Hand Limits
• ▸Existence of a Limit
• ▸Intuitive Evaluation of Limits

Chapter Summary

--- PAGE 1 --- Chapter 12 LIMITS AND DERIVATIVES ⁂ With the Calculus as a key, Mathematics can be successfully applied to the explanation of the course of Nature – WHITEHEAD ⁂ 12.1 Introduction This chapter is an introduction to Calculus. Calculus is that branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain change. First, we give an intuitive idea of derivative (without actually defining it). Then we give a naive definition of limit and study some algebra of limits. Then we come back to a definition of derivative and study some algebra of derivatives. We also obtain derivatives of certain standard functions. 12.2 Intuitive Idea of Derivatives Physical experiments have confirmed that the body dropped from a tall cliff covers a distance of 4.9t² metres in t seconds, i.e., distance s in metres covered by the body as a function of by s = 4.9t². Sir Issac Newton (1642-1727) The adjoining Table 13.1 gives the distance …

Practice Questions from this Chapter

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1. Explain instantaneous velocity simply? Get Solution →
2. Visualize what a limit means? Get Solution →
3. Show everyday examples of rates of change? Get Solution →
4. According to the introduction, what is the primary focus of Calculus? Get Solution →
5. What is the formula given for the distance 's' in metres covered by a body dropped from a tall cliff in 't' seconds? Get Solution →
6. How is the average velocity between time t₁ and t₂ calculated? Get Solution →
7. What is the general symbolic representation for 'the limit of f(x) as x approaches a equals l'? Get Solution →
8. What is the term for the expected value of a function at x=a based on the values of the function for x > a? Get Solution →

Did you know?

• 💡 Calculus was co-invented by Isaac Newton and Gottfried Leibniz around 1670.
• 💡 Honeybees use advanced math to find the most efficient route between flowers.
• 💡 The concept of zero was developed to represent the absence of quantity, a mathematical limit.
• 💡 Zeno's paradoxes explored early ideas of limits and infinity with puzzles.
• 💡 Weather forecasts use complex calculus to predict how atmospheric conditions change.

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