Exercise 2B:Q2 (a), (b), (c), (d), (e) & (f)
Q6 (a), (b), (c) & (d)
Exercise 2E:Q5 (a) (i), (ii) & (iii)
(b) (i), (ii) & (iii)Q6 (a), (b) & (c)
Q10 (a) & (b)
Example (Chapter 3 Differentiation):
Find the first derivatives for the following functions:
(a)
Answer:
(b)
Answer:
(c)
Answer:
(d)
Answer:
Examples of rate of change:Q1Each edge of a variable cube is
increasing at a rate of 3 cm per second. How fast is the volume of
the cube increasing when the edge is 12 cm long?
Q2All edges of a cube are expanding at a rate of 1.5 cm per
second. How fast is the surface area changing when each edge is 8
cm?
Q3Assume that oil spilled from a ruptured tanker spreads in a
circular pattern whose radius increases at a constant rate of 2
ft/sec. How fast is the area of the spill increasing when the
radius of spill is 60 ft?
Q4A spherical balloon is to be deflated so that its radius
decreases at a constant rate of 15 cm/min. At what rate must air be
removed when the radius is 9 cm?
Q5A spherical balloon is being filled with a gas in such a way
that when the radius is 20 cm, the radius is increasing at the rate
of . How fast is the volume changing at this time?Q6A 13-cm ladder
is leaning against a wall. If the top of the ladder slips down the
wall at a rate of 2 cm/s, how fast will the foot be moving away
from the wall when the top is 5 cm above the
ground?_1447110824.unknown
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