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Taylor's Theorem - 1 Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

Q: 3. What is the formula for Taylor's theorem?

Ans. The formula for Taylor's theorem is:f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...where f(x) is the function we want to approximate, a is the point around which we are approximating, and f'(a), f''(a), f'''(a), etc., are the derivatives of the function evaluated at the point a.

FAQs on Taylor's Theorem - 1 Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

1. What is Taylor's theorem?

Ans. Taylor's theorem is a mathematical theorem in calculus that gives an approximation of a function using its derivatives at a single point. It states that any smooth function can be approximated by a polynomial function near a given point.

2. How is Taylor's theorem used in calculus?

Ans. Taylor's theorem is used in calculus to approximate the value of a function at a particular point using information about the function's derivatives at that point. It allows us to estimate the behavior of a function by representing it as a polynomial.

3. What is the formula for Taylor's theorem?

Ans. The formula for Taylor's theorem is: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ... where f(x) is the function we want to approximate, a is the point around which we are approximating, and f'(a), f''(a), f'''(a), etc., are the derivatives of the function evaluated at the point a.

4. What is the significance of Taylor's theorem in calculus?

Ans. Taylor's theorem is significant in calculus because it provides a way to approximate complex functions using simpler polynomial functions. It allows us to study the behavior of functions and make predictions about their values without having to rely on the original, often more complicated, function.

5. Can Taylor's theorem be used to find the value of any function at any point?

Ans. Taylor's theorem can be used to find the value of a function at any point, but the accuracy of the approximation depends on the number of terms included in the polynomial. The more terms we include, the closer the approximation will be to the actual value of the function. However, calculating higher-order derivatives can be computationally complex, so in practice, Taylor approximations are often used with a limited number of terms.

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Sep 09, 2025 Last updated

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