# Finding the values of k???

• Mar 31st 2008, 02:20 AM
federer
Finding the values of k???
Let f be a piecewise defined function given by
f(x) ={ k(k + 1) sin² (x) + 2e^kx cos(x), x < (π÷2),
{ x² + k (x - k + 1), x ≥ (π÷2)

for some k Є R. Find the values of k for which f is continuous when x = (π÷2).

please solve this including showing the workings.
The 2 individual { brackets are supposed to be 1 large bracket but there is no large bracket sign i can use,so i used 2 { instead indicating just 1 {.
Hope u understand what im saying.
Try to show the workings and give a clear answer so i dont get confused with the whole thing.
÷ Є ∞ ○ π { ≤ ² ≥ ∩
• Mar 31st 2008, 06:38 AM
CaptainBlack
Quote:

Originally Posted by federer
Let f be a piecewise defined function given by
f(x) ={ k(k + 1) sin² (x) + 2e^kx cos(x), x < (π÷2),
{ x² + k (x - k + 1), x ≥ (π÷2)

for some k Є R. Find the values of k for which f is continuous when x = (π÷2).

please solve this including showing the workings.
The 2 individual { brackets are supposed to be 1 large bracket but there is no large bracket sign i can use,so i used 2 { instead indicating just 1 {.
Hope u understand what im saying.
Try to show the workings and give a clear answer so i dont get confused with the whole thing.
÷ Є ∞ ○ π { ≤ ² ≥ ∩

Since both parts of the function are continuous on the relevant regions to
make the function continuous you need only that they are equal at n/2.

So you need to solve:

k(k + 1) (sin(n/2))^2 + 2e^(kn/2) cos(n/2)=n^2/4 + k (n/2 - k + 1)

for k.

RonL