Differentiation to determine rate of change when voltage is given

Calculus

Table of Contents
TASK 1............................................................................................................................................1
Differentiation to determine rate of change when voltage is given.............................................1
TASK 2............................................................................................................................................4
PART 1........................................................................................................................................4
PART 2........................................................................................................................................5
TASK 3............................................................................................................................................6
PART 1........................................................................................................................................6
PART 2........................................................................................................................................6
TASK 4............................................................................................................................................7
PART 1........................................................................................................................................7
PART 2........................................................................................................................................8

TASK 1
Differentiation to determine rate of change when voltage is given
(a) v = (t2 + 6)2
r = dv/dt
= d (t2 + 6)2
dt
= 2 (t2 + 6). 2t
= 4t (t2 + 6)
at t = 5 sec, rate of change will be
r = 4 x 5 (52 + 6)
= 20 (31) = 620 units
(b) v = (3t3 – 4t + 6)3
r = dv/dt
= d (3t3 – 4t + 6)3
dt
= 3 (3t3 – 4t + 6)2. (9t2 – 4)
= 3(9t2 – 4) (3t3 – 4t + 6)2
at t = 5 sec, rate of change will be
r = 3(9.52 – 4) (3.53 – 4.5+ 6)2
= 3 (221) (361)2
≈ 8.6 x 107 units
1