Limx →0 (√(1+x)-√(1-x))/(x){ Ans. (2)/(3)}

Name: Problem 91, Chapter 2: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-09-10T08:02:48-08:00
Duration: 3 min 53 s
Channel: Anurag Kumar
Description: limx →0 (√(1+x)-√(1-x))/(x){ Ans. (2)/(3)}

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Key Concepts

Radical Functions with Fractional Exponents

Radical functions with fractional exponents, such as cube roots or square roots, can be rewritten in the form (1 + x)^(1/n). Understanding these functions is crucial in calculus, as their behavior under limits and differentiation often requires special techniques like series expansion or the application of derivative rules.

Derivative

A derivative represents the instantaneous rate of change of a function with respect to its variable and is defined as the limit of the difference quotient. It is a central concept in calculus that helps in understanding how functions change and is used to find slopes of tangent lines and to model dynamic systems.

Limit

A limit describes the value that a function approaches as the input approaches a particular point. It is a fundamental concept in calculus, providing the basis for understanding continuity, derivatives, and integrals by rigorously examining the behavior of functions near specific points.

Binomial Series Expansion

The binomial series expansion is a method for expanding expressions of the form (1 + x)^r, where r can be any real number, into an infinite series. This technique is especially useful for approximating functions near a point, simplifying the process of finding limits and derivatives for functions with fractional exponents.

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