Introduction to Limits: Part 1 Video Lecture | Mathematics (Maths) Class 11 - Commerce

Ans. In calculus, a limit is a fundamental concept that describes the behavior of a function as its input approaches a certain value or as it tends towards infinity or negative infinity. It determines the value a function approaches or tends to, even if it may never actually reach that value.

Ans. To find the limit of a function, you can evaluate the function at various values close to the desired point and observe the pattern. If the function approaches a specific value as the input values get closer and closer to the desired point, that value is the limit. Alternatively, you can use algebraic techniques such as factoring, rationalizing, or applying known limit rules to simplify the function and determine its limit.

Ans. There are several types of limits commonly encountered in calculus: - Finite limits: These limits exist when the function approaches a specific finite value as the input approaches a certain point. - Infinite limits: These limits occur when the function grows without bound as the input approaches a certain point, either positive or negative infinity. - One-sided limits: These limits consider the behavior of a function as the input approaches a certain point from either the left or the right side. - Discontinuous limits: These limits occur when the function has a jump or a hole at the desired point, resulting in different limits from each direction.

Ans. There are several common limit rules in calculus that help simplify the evaluation of limits: - Sum/Difference Rule: The limit of the sum or difference of two functions is equal to the sum or difference of their respective limits. - Product Rule: The limit of the product of two functions is equal to the product of their respective limits. - Quotient Rule: The limit of the quotient of two functions is equal to the quotient of their respective limits, provided the limit of the denominator is not zero. - Power Rule: The limit of a power of a function is equal to the power of the limit of the function. - Chain Rule: The limit of a composite function is equal to the limit of the outer function evaluated at the limit of the inner function.

Ans. Limits are extensively used in calculus to study the behavior of functions, determine continuity, find derivatives, and solve various problems. They help analyze the rate of change, the slope of curves, and the behavior of functions near critical points. Limits are essential in understanding fundamental concepts like derivatives, integrals, and differential equations, making them crucial for applications in physics, engineering, economics, and other fields.