Solutions Sheet 3, Differentiation Questions 28-42 Solutions to ...

• cours magistral

Solutions Sheet 3, Differentiation Questions 29-44 Solutions to Additional Questions 29) Set f (x) = sin ( (3 + x)2 ) , then f (x)− f (0) x− 0 = sin ( (3 + x)2 ) − sin 9 x . So lim x→0 sin ( (3 + x)2 ) − sin 9 x = f ′ (0) . The function f (x) is the composite of sin y and y = (3 + x)2 , both of which are differentiable.

• positive square root
• result from part
• composite rule for differentiation
• difference of the derivatives
• difference of the nth-terms
• sandwich rule
• additional questions
• sin
• part
• value