Where Does \(\frac{1}{2}x\) Come From at \(k=1\)?

[izen]

Homework Statement

How did \frac{1}{2}x come from at k=1?

Homework Equations

The Attempt at a Solution

because k=1 will make the first term at denominator 2(k-1) = \frac{0}{0}

 

[SammyS]

Homework Statement

How did \frac{1}{2}x come from at k=1?

Homework Equations

The Attempt at a Solution

because k=1 will make the first term at denominator 2(k-1) = \frac{0}{0}

Yes. The \ \frac{1}{2}x\ comes from the fact that the first term has the form 0/0 as k → 1.

What is \displaystyle \ \lim_{t\to0}\frac{\sin(t)}{t}\ ?

 

[izen]

Yes. The \ \frac{1}{2}x\ comes from the fact that the first term has the form 0/0 as k → 1.

What is \displaystyle \ \lim_{t\to0}\frac{\sin(t)}{t}\ ?

Use L' Hopital's Rule --> \displaystyle \ \lim_{t\to0}cos(t) = 1

thank you SammyS