-
Q1 Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Ans: Our Experts will give the answer soon.
Welcome to the Chapter 5 - Continuity and Differentiability, Class 12 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 5 - Continuity and Differentiability.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics and excel in their exams. By going through these Continuity and Differentiability question answers, you can strengthen your foundation and improve your performance in Class 12 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
In the previous class, introduction of limits and derivatives was given. That was basically a calculus introduction. This chapter is a continuation of it. We will study about differentiation of functions. New functions like exponential and logarithmic functions will be introduced. This chapter consists of continuity and differentiability. derivative of a composite function, chain rule, derivatives of inverse trigonometric functions and implicit functions, logarithmic differentiation, parametric forms of derivative of functions, second order derivatives, Rolle's and Lagrange's Mean value theorems.
Q1 | Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5. |
Ans: | Our Experts will give the answer soon. |
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0
A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
Let f : R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?