A chemical reaction produces a foam whose volume VVV (in cm3\text{cm}^3cm3) changes at a rate V′(t)V'(t)V′(t) where t t\,t is the time in seconds since the start of observation, for t>0t > 0t>0.
Given that
(i) Find the value of the gradient of the curve at PPP.
(ii) Hence find the equation of the tangent to the curve at PPP, giving your answer in the form at+bV+c=0at + bV + c = 0at+bV+c=0, where aaa, b b\,b and c c\,c are integers to be found.
Find g(t)g(t)g(t), simplifying your answer.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
