00:01
In this problem we are asked to estimate the limit h tends to 0 4 raised to the power of h minus 1 the whole divided by h by considering values for h.
00:16
So first let us consider the left -hand limit.
00:19
That is, we consider values of h that approach 0 from the left.
00:24
So let us consider the value of h to be negative 1.
00:27
In that case we have 4 raised to the power of h minus 1 the whole divided by h to be equal to 4 raise to the power of negative 1 minus 1 the whole divided by negative 1 which on evaluating equals to 0 .75.
00:45
Next let us consider h to be negative 0 .5.
00:49
So we have 4 raised to the power of negative 0 .5 minus 1 the whole divided by minus 0 .5 which on evaluation gives us.
00:57
Gives the answer as 1.
00:59
Next we consider h to be negative 0 .1.
01:02
So we have 4 raised to the power of negative 0 .1 minus 1 the whole divided by minus 0 .1 which on evaluation is equal to 1 .295.
01:16
Next let us consider the value of h to be negative 0 .01 and the corresponding value is given by 4 raised to the power of negative 0 .01 minus 1 the whole divided by negative 0 .01 which on evaluation is 1 .37673 approximately.
01:40
Next let us consider h to be 0 .001 so we have 4 raised to the power of negative 0 .001 minus 1 the whole divided by negative 0 .001...