13 - Curriculum Development Centre, Kalamassery

3) limit x² – 3xx->3 x² - 93.1.4 verify the following results1) limit x n – a n = n a n- ¹, when n is rationalx->a x – a2) limit Sin = 1, is in radianø ->0 ø3.1.5 Solve problems of the type1) Limit √x - √ax->a x - a2) limit Sin møø->0 ø3.1.6 Describe the general definition of continuous functions3.2 Methods of Differentiation – I3.2.0 Apply the methods of differentiation3.2.1 Define the derivative of a function y = f(x) as limit ∆y∆x->0 ∆x3.2.2 Show the geometrical concept of derivatives3.2.3 Find the derivatives of x n , Sinx, and Cosx from first principles3.2.4 State the rules of differentiation1) Sum or difference2) Product3) Quotient3.2.5 Find derivatives of e x and log n. State all the fundamental formulae3.2.6 Apply the rules and differentiate simple functions of the type1) x² sec x2) tan xx² + 13) x Cosec x3x – 23.3 Methods of Differentiation – II3.3.0 Apply different methods of differentiation3.3.1 Find the derivatives if the functions of the form[f(x)] n , Sin f(x), Cos f(x), with respect to x.3.3.2 Find the derivatives ofe Sinx , log sinx, (x²+1) 10 Sec5x, Sin 2x, Cot 5 (x³), log (sec x + tan x)1+cos2x3.3.3 Find the derivative of the implicit functions of the formax² + 2hxy + by² = 03.3.4 Differentiate parametric functions of the typex = f(x), y = g(t)3.3.5 Find the second derivative of the functionsy = x , y = x² sinxx-23.3.6 Solve the problem of the typeIf y = x 2 cos x, show thatx² d²y – 4x dy + (x²+6) y = 0dx² dxUNIT – IV4.1 Applications of Differentiation4.1.0 Apply the theories of differentiation in different problems4.1.1 State geometrical meaning of derivatives18