Recall that for |<em>x</em>| < 1, we have
Differentiating both sides gives
and multiplying both sides by 8 gives the series for <em>f(x)</em> :
and this converges over the same interval, |<em>x</em>| < 1, so that the radius of convergence is 1.
An hour and twenty minutes
The scientific notation is a method that scientists use
to easily handle very large numbers or very small numbers. As an example,
instead of writing down the value 0.0000000065, we write the value 6.5 x 10-9
in scientific notation. The number of places the decimal point got moved
becomes the exponent of the number 10. When the movement is from left to right,
the exponent is negative (for very small numbers). When it is right to left,
the exponent is positive (for very large numbers).
Therefore writing estimated measurements in scientific
notation:
length of a grain of salt : 0.0002 centimeters = 2 x 10-4
centimeters
width of a key ring : 0.02 centimeters = 2 x 10-2
centimeters
C: -14 Makes the statement true.
