The vertical profile of a survey drone is modeled by a curve CCC with equation h=f(t)h = f(t)h=f(t), t>0t > 0t>0, where hhh is the altitude in meters and ttt is the time in seconds. The drone passes through the point P(4,10)P(4, 10)P(4,10).
Given that f′(t)=3t+2−16t2\displaystyle f'(t) = 3\sqrt{t} + 2 - \frac{16}{t^2}f′(t)=3t+2−t216
Find the equation of the normal to CCC at PPP. Write your answer in the form at+bh+c=0at + bh + c = 0at+bh+c=0, where aaa, bbb and ccc are integers to be found.
Find f(t)f(t)f(t).
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
