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Sub-topics: 8.1 Informal discussion of continuity. (1) 8.2 The notion of the limit of a function and the definition of continuity in terms of this notion. (3) 8.3 Gradient of a secant to the curve y = f(x). (3) 8.4 Tangent as the limiting position of a secant. The gradient of the tangent. Equations of t… (3) 8.5 Formal definition of the gradient of y = f(x) at the point where x = c. Notations f '(c),… (3) 8.6 The gradient or derivative as a function. Notations f '(x), , (f(x)), y' (4) 8.7 Differentiation of xn for positive integral n. The tangent to y = xn. (2) 8.8 Differentiation of and x–1 from first principles. For the two functions u and v, different (1) 8.9 Differentiation of: general polynomial, xn for n rational, and functions of the form … (2)
