4.3 Reinforcement
4.3.1 y=an,n=an integer
➤➤
119 120➤A.Plot the values of 3nforn=−2,−1, 0, 1, 2, using Cartesian axes withnon the
horizontal axis and 3non the vertical axis.
B.Plot the graphs ofy= 3 xandy= 4 xon the same axes. Sketch the graph ofy=πx.
4.3.2 The general exponential functionax
➤➤
119 121➤Simplify(i)8 x× 23 x
43 x(ii)6x(^2) × 12 x+^1 × 27 −
x
2
32
x
2
(iii)
x−
1
(^3) y−
2
3
(x^2 y^4 )−
1
6
(iv)
x^2 (x^2 + 1 )−
1
(^2) −(x^2 + 1 )
1
2
x^2
(v)
exe−x
2
ex−^1 e(x+^1 )^2
(vi)
a^3 a−(x+^1 )
2
a−x^2 a−^2 x
(vii)
acos 2xa−cos
(^2) x
a^3 −sin
(^2) x
4.3.3 The natural exponential functionex
➤➤
119 124
➤
A.Referring to the ‘interesting’ Problem 2 in Section 4.2.3, determine the debt owing if
interest is reckoned by the (i) minute (ii) second.
B. Use the series forexto evaluate to 4 decimal places (i)e, (ii)e^0.^1 , (iii)e^2.
C.Sketch the curves
(i) y=ex− 1 (ii) y= 1 −e−x
D.Solve the equation
e^2 x− 2 ex+ 1 = 0
4.3.4 Manipulation of the exponential function
➤➤
119 129
➤
Simplify
(i) eA(eB)^2 e^3 C (ii)
exe^3 y(ex)^2
e−xey
(iii)
(ex)^3 ex
2
(ey)^2
e^4 yex+^3
(iv)
(eB)^2 eAeB−^2
e^2 −Be^2 A
(v)
(eA+e−A)^2
e^2 A
(vi)
(eA+e^3 B)(e−A+e−B)
e^2 BeA