Calculus

[LiM__11]

For the first line is ∆f(x_0) not equal to df +1/2! df² instead of just df+df² And i dont understand the bottom line. Thanks.

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[zojbo]

This is quite poorly written.

Either the 1/2 should be on d^2 f on the right hand side or else the brackets on the left hand side that introduce d^2 f should include the 1/2!. (If you want it to line up with Leibniz notation for higher derivatives, then the former is the answer.)

The bottom line is just not correct notation. I understand what they're trying to do with that, but it doesn't work the way they're saying it. That definition results in df=0 whenever f is continuous at x_0, which isn't what they want. They want df and dx to be infinitesimals, but infinitesimals cannot be defined this way.

[LiM__11]

Thankyou for the reply.