Solutions Sheet 3, Differentiation Questions 19-28 v2

• cours magistral

Solutions Sheet 3, Differentiation Questions 19-28 v2 19) Go back to the definition and for x 6= 0 consider f (x)− f (0) x− 0 = sinx x − 1 x = sinx− x x2 = x sinx− x x3 . Thus, by the Product Rule, lim x→0 f (x)− f (0) x− 0 = lim x→0 x sinx− x x3 = ( lim x→0 x )( lim x→0 sinx− x x3 ) = 0× ( − 1 6 ) = 0.

• stated result by x3 gives
• stated result
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