Question

Find k so that the following function is continuous on any interval. h(x)= kcosx if 0≤x≤9pi h(x)= 12-x if 9pi 11 years ago

Answer 1

please someone help me! I've been stuck for the longest time and the answer that I get is incorrect :(

Answer 2

@ecarreno The last inequality doesn't make sense to me
9pi<0?

Answer 3

maybe you meant x>9pi?

Answer 4

@myininaya Yes oops sorry.

Answer 5

If so, it makes sense to me...
And
what you need is the following:
If h is continuous at x=9pi then you have the following:
a) \[\lim_{x \rightarrow 9 \pi} h(x) \text{ exists } \]
For this to exist you must have the left limit equal the right limit.
b) \[h(9 \pi) \text{ exists }\]
and finally c)
You want the number you get from a to equal the number you got from b.


Let's start off with the left limit equaling the right limit

Answer 6

\[\lim_{x \rightarrow 9\pi^+}h(x)=\lim_{x \rightarrow 9\pi^-}h(x)\]

Answer 7

Evaluate both sides first. Then solve the equation.

Answer 8

I don't understand which equation? this is how I was solving it, please tell me if it's the correct way...
kcosx=12-x
kcos9pi=12-9pi
-k=12-9pi
k=-12+9pi

Answer 9

\lim_{x \rightarrow 9\pi^+}h(x)=\lim_{x \rightarrow 9\pi^-}h(x)
I was talking about this equation....
But yeah you went about it correct you can plug in 9pi because both of the functions are continuous at 9pi

Answer 10

\[\lim_{x \rightarrow 9\pi^+}h(x)=\lim_{x \rightarrow 9\pi^-}h(x)\]

To evaluate the right limit you get 12-9pi
To get the left limit you get kcos(9pi)
So \[\lim_{x \rightarrow 9\pi^+}h(x)=\lim_{x \rightarrow 9\pi^-}h(x)\]
we can rewrite this equation as:
12-9pi=kcos(9pi)
Then solve for k

Answer 11

Okay my answer is -12+9pi after I solve for k and the online calc book I am using tells me that it is incorrect.

Answer 12

Did they write 9pi-12?

Answer 13

Because that is the same thing

Answer 14

No, it won't show me the answer unless I use up all of my attempts.. I am down to my last attempt

Answer 15

I don't know if they want an approximation or not
but your answer is fine in the exact form

Answer 16

it was 9pi+12, thank you:)

Answer 17

I think the computer or the test maker made an error in that answer

Answer 18

oops I meant 9pi-12

Answer 19

It should be 9pi-12

Answer 20

But you know that is the exact answer you put

Answer 21

Just in a different order

Answer 22

9pi-12
is
-12+9pi

Answer 23

yeah, but i guess the online book wants it in a specific order..

Answer 24

Ok. Coolness.