Question

I'm confused on how to solve this...Find the limit of the function by using direct substitution.

limit as x approaches quantity pi divided by two of quantity three times e to the x times cosine of x.

Answer 1

Here's a hint...since everything is multiplied together..

what is \(\large \cos(\pi/2)\)?

Answer 2

0

Answer 3

right...and since 0is being multiplied, we know the whole function approaches 0 as x goes to pi/2

Answer 4

where do i plug in 0

Answer 5

\[\large 3e^\frac{\pi}{2}\cos(\frac{\pi}{2})\] is what is meant by direct substitution
i.e. plug it in

Answer 6

so it's 3e^0*0 and that gives 0

Answer 7

No, the 'x' you plug in is \(\large \frac{\pi}{2}\)

so really it would be as satellite put above

\[\large 3e^{\frac{\pi}{2}}cos(\frac{\pi}{2})\]

And since we know that \(\large cos(\frac{\pi}{2}) = 0\)

we have

\[\large 3e^{\frac{\pi}{2}} \times 0\]

which we know will be 0 since anything times 0 = 0

Answer 8

ohhh okay got it thanks :)

Answer 9

Anytime! :)