Topic: Further Differentiation (A level Maths)

2. (a) Show from first principles that for the curve y = sinx, where x is in radians, dy - = COS X . dx You may use the formula for sin ( AtB) without proof and assume that as h -> 0, cosh -1 sin h ->0 and -1. [5] h h (b) Identify where in the proof this assumption that x is in radians is needed. [1] 3. (a) Find an expression in terms of x and y for the gradient of the curve x' + kxy+42 =48 [3] (b) The diagram shows the curve where k = 2. Find the values of y for which the tangent to the curve is vertical. [3] (c) Explain what happens to the gradient when k =4. [1]