Plane trigonometry, by S.L. Loney.

336 TRIGONOMETRY.
Ex. 2. Find the value, when x is zero, of the expression
cosx- loge(1 + x) +sinx - 1
e - (1 --- x)
Since loge (l+x)= x- xx2 +3- 4..
22 3 4a4
X2 'X3 X4
and ex=l1+x- + 1 3 +- (Arts. 253 and 256),
this expression
_ X - q X3 X
(x2 x4 + ( 3 f
x2 X3
1+++h2+e + p)-(o1+o)
1
X3 X
-2 +higher powers of x +powers of x
x2 1
- + higher powers of x o + powers of x
\1 I2
When x is zero, this latter expression
0
= =0.
Ex. 3. Find the value, when x is zero, of
(tan xx
When x is zero, this expression is of the form (0j
x+-s+ s...
But it also =- (Art. 281).
Now, by Art. 250, the value of

is e, when x is zero.
Hence the expression = e 3 = e~ =1.
The value of the expression may be also found by finding the value of
its logarithm.