THE NATURAL LOGARITHM 0 193
So,
23.68 Evaluate
23.69
Evaluate
23.71
Evaluate
23.72
Evaluate
23.75
Solve the equation 5 In x + 2x = 4 + In x
5 for x.
5In x + 2x = 4 + 5 Inx, 2x = 4, x=2.
23.76
Sketch the graph of y = 3x + 1 - 5 In (1 + x
2 ).
See Fig. 23-8.
23.74
Solve the equation 3 In x = In 3* for x.
3 In x = In 3x = In 3 + In x, 2 In x = In 3, In x
2 = In 3, x
2 = 3, x = VI.
The points of subdivision are
Then Simpson's rule yields
(Compare this with the result of Problem 23.57.)
23.73 Estimate In 2 =
by Simpson's rule, with n = 4.
Let h=2x-f,. Then the given limit is
23.67
If y = (1 - 3x
2 )
3 (cos 2x)\ find y'.
Use logarithmic differentiation. In y = 3 In (1 - 3x
2 ) + 4 In (cos 2x). Hence,
In
In
In
In
In
In
23.70 find the area under
between
and
Hence, the area is
In