00:01
The question is estimate using the linear approximation and find the error using a calculator.
00:05
So the expression we're given is 1 over root 98 minus 1 over 10.
00:11
So we can set f of x equal to 1 over root x, where a equals 100 and delta x is equal to negative 2.
00:42
So this is the linear approximation, and we want to find an estimate for delta f, which we would need f prime at point a multiplied by delta x.
00:57
So since we're already given delta x, we want to find the derivative of f of x at point a.
01:05
So in order to do this, we can use the power down rule, so we can re -referred.
01:11
Write 1 over root x as x to the negative 1 half to make it more clear to use the power down rule.
01:23
And so the derivative of x to the negative 1 half, you would bring down the negative 1 half, and you would have x to the negative 3 halves...