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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 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.
Download pdf of NCERT Solutions for Class Mathematics Chapter 5 Continuity and Differentiability
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.
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 Signum Function f : R → R, given by
is neither one-one nor onto.
Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0
Determine order and degree(if defined) of differential equation \begin{align}\frac{d^2y}{dx^2}=\cos3x + sin3x\end{align}
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.