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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.
Let f : R → R be defined as f(x) = 3x. 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.
y = cosx + C : y' + sinx = 0
Classify the following measures as scalars and vectors.
(i) 10 kg (ii) 2 metres north-west (iii) 40°
(iv) 40 watt (v) 10–19 coulomb (vi) 20 m/s2
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
Classify the following as scalar and vector quantities.
(i) time period (ii) distance (iii) force
(iv) velocity (v) work done
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}
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.