Le^x-(1+x/1+x^2/2)l <= e/6 for all x E [0,1].

[squenshl]

I have a problem.
How do I show that le^x-(1+x/1!+x^2/2!)l <= e/6 for all x E [0,1].

 

[Phrak]

Show that the equation is true at the boundries. Show that the term on the left is monotonic in x (if, indeed, it is).

 

[adriank]

What a strange coincidence. I saw this thread only after posting my example in this thread.

If you don't want to see the full solution, here's a hint: Taylor's theorem.

 

[ice109]

how to show that a function is monotonic increasing? show that f(x+1) >= f(x) for all x?

 

[dx]

how to show that a function is monotonic increasing? show that f(x+1) >= f(x) for all x?

No, that won't work. A function is monotonic increasing if f(x) ≥ f(y) whenever x ≥ y.