Introduction to Limits- 2 Video Lecture | Calculus - Mathematics

Ans. In calculus, a limit is a fundamental concept that describes the behavior of a function as the input approaches a particular value or as it tends to infinity. It signifies the value that a function is approaching or getting arbitrarily close to, without actually reaching that value.

Ans. To find the limit of a function, you need to evaluate the function as the input approaches the desired value. This can be done by direct substitution if the function is defined at that point. If the function is not defined at that point, you can use algebraic manipulations, factoring, or rationalizing techniques to simplify the expression and then substitute the value.

Ans. There are several types of limits in calculus, including: - Finite Limit: This occurs when the function approaches a specific finite value as the input approaches a particular value. - Infinite Limit: This occurs when the function approaches infinity or negative infinity as the input approaches a particular value. - One-Sided Limit: This occurs when the function approaches different values from the left and right sides of a point. - Limit at Infinity: This occurs when the function approaches a specific value as the input approaches infinity or negative infinity.

Ans. Limits are significant in calculus as they allow us to analyze the behavior of functions and study their properties. They help determine continuity, differentiability, and integrability of functions. Limits also enable us to solve various mathematical problems, such as finding the slope of a curve, determining the rate of change, or calculating instantaneous velocity.

Ans. There are several common techniques to evaluate limits, including: - Direct Substitution: This involves substituting the desired value directly into the function and evaluating the resulting expression. - Factoring: This technique involves factoring the expression and canceling out common factors to simplify the function. - Rationalizing: This technique is used when the function involves radicals or fractions. It involves multiplying the expression by the conjugate to eliminate radicals or simplify fractions. - L'Hôpital's Rule: This rule is used for indeterminate forms, such as 0/0 or ∞/∞. It involves taking the derivative of the numerator and denominator separately and then evaluating the limit again. - Squeeze Theorem: This theorem is used when the function is bounded between two other functions. It allows us to determine the limit of the function by considering the limits of the bounding functions.