Differentiation Important Questions Class 12

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WEB Continuity and Differentiability Class 12: Important Questions with Solutions

Introduction

Continuity and differentiability are fundamental concepts in calculus that play a crucial role in understanding the behavior of functions. For class 12 students, mastering these concepts is essential for success in mathematics.

Continuity

A function f(x) is said to be continuous at a point x = a if the following three conditions are met:

• f(a) exists.
• lim_x->a f(x) = f(a).
• lim_h->0 f(a + h) = f(a).

Differentiability

A function f(x) is said to be differentiable at a point x = a if the limit of the difference quotient as h approaches 0 exists:

lim_h->0 [f(a + h) - f(a)] / h

If the limit exists, it is called the derivative of f(x) at x = a and is denoted by f'(a).

Important Questions with Solutions

Here are some important questions on continuity and differentiability in class 12 with solutions:

1. Find the points of discontinuity of the function f(x) = |x - 2|.
2. Prove that the function f(x) = sin x is continuous at every point.
3. Find the derivative of the function f(x) = e^2x.
4. Find the equation of the tangent to the curve y = x³ + 2x at the point (1, 3).

Answers to these questions can be found in standard textbooks or online resources.

Conclusion

Understanding continuity and differentiability is essential for students of mathematics and related fields. By mastering these concepts and practicing the important questions provided, students can improve their problem-solving skills and prepare for examinations.

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