Class 12 Mathematics — Chapter 5: CONTINUITY AND DIFFERENTIABILITY

What you'll learn

• ▸Intuitive Concept of Continuity
• ▸Formal Definition of Continuity at a Point
• ▸Left-Hand and Right-Hand Limits in Continuity
• ▸Identifying Points of Discontinuity
• ▸Continuity over an Interval
• ▸Continuity of Standard Functions
• ▸Concept of Infinite Limits

Chapter Summary

--- PAGE 1 --- Chapter 5 CONTINUITY AND DIFFERENTIABILITY ✦ The whole of science is nothing more than a refinement of everyday thinking." — ALBERT EINSTEIN ✦ 5.1 Introduction This chapter is essentially a continuation of our study of differentiation of functions in Class XI. We had learnt to differentiate certain functions like polynomial functions and trigonometric functions. In this chapter, we introduce the very important concepts of continuity, differentiability and relations between them. We will also learn differentiation of inverse trigonometric functions. Further, we introduce a new class of functions called exponential and logarithmic functions. These functions lead to powerful techniques of differentiation. We illustrate certain geometrically obvious conditions through differential calculus. In the process, we will learn some fundamental theorems in this area. 5.2 Continuity We start the section with two informal examples to get a feel the function …

Practice Questions from this Chapter

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1. Draw a graph without lifting your pen? Get Solution →
2. Explain why some functions have sharp corners? Get Solution →
3. Describe a real-world example of continuity? Get Solution →
4. According to Definition 1, when is a function f considered continuous at a point c? Get Solution →
5. The text states that the constant function, f(x) = k, is continuous at which points? Get Solution →
6. Based on Example 6, what is the continuity status of the identity function, f(x) = x? Get Solution →
7. What does the text informally suggest about the graph of a continuous function? Get Solution →
8. According to Definition 2, when is a real function f said to be a 'continuous function'? Get Solution →

Did you know?

• 💡 The equals sign (=) was invented in 1557 to avoid writing "is equal to".
• 💡 A Mobius strip is a surface with only one side and one continuous boundary.
• 💡 Isaac Newton, who developed calculus, also studied the speed of sound.
• 💡 The number zero was once not considered a number but a placeholder.
• 💡 Calculus is vital for designing roller coasters to ensure smooth, continuous rides.

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