Explore the mathematical journey of finding the value of the nth derivative of y = 1-x/1+x. This guide provides a clear and concise solution, taking you through the differentiation process with precision and clarity. Question 6:- Find the value of , where . Solution:-Given that, Differentiate with respect to x ⇒ ⇒ ⇒ Again differentiate … Read more
The mathematical exploration of finding If y = Sin³ x find nth term of y, a compelling journey through trigonometry and calculus. This solution not only simplifies the expression to a well-known trigonometric identity but also navigates through the process of differentiation, partial fractions, and the intriguing use of complex numbers. Question 5:- If y … Read more
Dive into the mathematical exploration of finding the nth derivative of Tan inverse 1 +x/1 -x, a compelling journey through trigonometry and calculus. This solution not only simplifies the expression to a well-known trigonometric identity but also navigates through the process of differentiation, partial fractions, and the intriguing use of complex numbers. Question 4:- Find … Read more
Explore the nth derivative of y If y = x²upon (x-1)² into (x + 2) through a step-by-step solution. Unravel the complexities of differentiation as we break down the process of finding the nth derivative of this trigonometric function. Question 3:- If , find the nth derivative of y. Solution:- Given, Using partial fraction ⇒ Clearing … Read more
Explore the nth derivative of tan¯¹ (x/a) through a step-by-step solution. Unravel the complexities of differentiation as we break down the process of finding the nth derivative of this trigonometric function. From the initial differentiation to the application of partial fractions, follow along as we navigate through the mathematical intricacies. Dive into the realm of … Read more
Learn how to find the nth derivative of x²/(x-a)(x-b) using the method of partial fractions. Follow the step-by-step solution to differentiate the function and obtain the desired result. Master the technique to find the nth derivative efficiently. Question 1:- Find the nth derivative of . Solution: Let Since. the given fraction is not a proper … Read more
Question 5:- Let f : R – {-4/3} → R be a function defined as f(x) = 4x/(3x+4). Show that, f:R – {-4/3} → Range of f, f is one-one and onto. [CBSE 2017(C)] Solution:- One-one: Let x, y ∈ R -{-4/3} Now, f(x) = … Read more
Question 6:- Let A = R – {3}, B = R – {1}. If f : A → B be defined by f(x) = {x – 2}/{x – 3}, ∀x ∈ A. Then, show that f is bijective. Solution:- Given that, A = R – {3}, B = R – {1}. f : A → … Read more
Question 7:- Let f : W → W, be defined as f(x) = x – 1, if x is odd and f(x) = x + 1, Show that f is bijective. Solution: One-one :- Case I : When x, y are even number Now, f(x) = f(y) ⇒ x + 1 = y + 1 … Read more
Question 4:- Consider → [4, ∞) given by f(x) = x² + 4. Show that f is invertible. [CBSE(AI) 2013] Solution:- One-one: Let x, y ∈ (Domain) such that f(x) = f(y) ⇒ x² + 4 = y² + 4 ⇒ x² = y² ⇒ x = y [∴ x, y are … Read more