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