anonymous one year ago Find the limit of the function by using direct substitution. lim(2e^x cos x) x-> pi/2

1. freckles

do you have a problem pluggin in pi/2?

2. anonymous

can you two help me

3. anonymous

i just have no idea how to solve this problem

4. freckles

$\lim_{x \rightarrow \frac{\pi}{2}}2e^x \cos(x)= 2 e^{\frac{\pi}{2}} \cos(\frac{\pi}{2})$ by direct substitution we can use direct substitution since the function exists at the thing the x is approaching

5. anonymous

im on the problem below

6. freckles

can you finishing simplifying

7. anonymous

thats the part i am having problems with.

8. freckles

so you aren't sure what cos(pi/2)=?

9. anonymous

-1/2

10. freckles

how do you get that

11. freckles

you can use the unit circle of the calculator if you want

12. freckles

cos(pi/2) should be zero either way

13. anonymous

oh

14. freckles

are you good?

15. freckles

$\lim_{x \rightarrow \frac{\pi}{2}}2e^x \cos(x)= 2 e^{\frac{\pi}{2}} \cos(\frac{\pi}{2}) \\ =2e^{\frac{\pi}{2}} (0)=?$