1
Q
sin0°
A
0
2
Q
sin30°/ 1/6 π
A
1/2
3
Q
sin45° / 1/4 π
A
√2
—
2
4
Q
sin60°/ 1/3 π
A
√3
—
2
5
Q
sin90°/ 1/2 π
A
√4
— = 1
2
6
Q
cos0°
A
√4
— = 1
2
7
Q
cos30°/ 1/6 π
A
√3
—
2
8
Q
cos 45° / 1/4 π
A
√2
—
2
9
Q
cos 60°/ 1/3 π
A
1/2
10
Q
cos 90°/ 1/2 π
A
0
11
Q
tan0°
A
0
12
Q
tan30° / 1/6 π
A
1
—
√3
13
Q
tan 45° / 1/4 π
A
1
14
Q
tan 60°/ 1/3 π
A
√3
15
Q
tan 90°/ 1/2 π
A
infinity
16
Q
log xy
A
log x + log y
17
Q
log x/y
A
log x - log y
18
Q
differentiate sin x
A
cos x
19
Q
differentiate cos x
A
-sin x
20
Q
differentiate tan x
A
sec²x
21
Q
gradient of normal when y=2x+3
A
-1/2
22
Q
find the values of x for which __ is an increasing function and dy/dx = (1-lnxl) /x²
A
find dy/dx
x² ≤ 0 ∀x
1-lnx>0
lnx<1
x<e>0 for the ln to be defined
∴ 0<x<e</e>
23
Q
steps to show that y is decreasing
A
find dy/dx
∵ __ ≤ 0 ∀x
For decreasing function, __< 0
24
Q
steps to find decreasing function
A
dy/dx
For decreasing function,
dy/dx value < 0
simplify < 0
sketch graph
inequality
25
2nd derivative for maximum
when y=__, d²y/dx²=__ <0
when y=__, it gives the maximum volume of the cylinder
26
given that y can vary, find value of y that gives the cylinder the max volume possible
dV/dy
For the stationary value of V, __ =0
d²y/dx² =__
when y= __, d²V/dy² =__<0
when y=__, it gives the maximum volume to the cylinder
