
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.
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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 each of the following cases, state whether the function is oneone, 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 + x^{2 }
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 oneone 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 oneone onto
(B) f is manyone onto
(C) f is oneone but not onto
(D) f is neither oneone nor onto.
y = cosx + C : y^{'} + sinx = 0
Classify the following measures as scalars and vectors.
(i) 10 kg (ii) 2 metres northwest (iii) 40°
(iv) 40 watt (v) 10^{–19} coulomb (vi) 20 m/s^{2}
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.