Question

Calc

Answer 1

In the xy-plane, the line -3x+9y=k, where k is a constant, is tangent to the graph of y=lnx, what is the value of k

Answer 2

@vocaloid help meeeeeeeeeeeeeeeeeeee

Answer 3

can u use a graphing calc

Answer 4

Well breaking it down and doing it step by step. What is the first step that we have to do to solve K

Answer 5

no, because the tests don't allow

Answer 6

could u like type the thing into desmos to get the answer, then afterwards get the teacher to elaborate on the topic so u can get a better understanding of it, unless darkknight fr boutta help

Answer 7

if i didnt have hw i would, sorry

Answer 8

also \[\lim_{x \rightarrow 2\pi} \frac{cosx-1}{x-2\pi}\] is it does not exist? because left hand limit is negative infinity and right is infinity?

Answer 9

calc is rusty, hope i did this right (?)

-3x+9y=k

let's re-arrange into y = mx + b form to make it simpler

y = (1/3)x + k/9

giving us slope 1/3.

at the tangent point, ln(x) also has slope 1/3. the derivative of ln(x) is 1/x, which is 1/3 at the tangent point. therefore x = 3 at the tangent point.

at the tangent point, the two functions also have the same value. if x = 3, then the linear function becomes: y = (1/3)(3) + k/9 and the other function becomes y = ln(3). you can set these equal to each other to solve for k.

Answer 10

I think you can use L'hopital's rule to get an actual limit on that limit problem

Answer 11

could I just write 9 ln3 -9 or should i find the decimal value?

we haven't learned l'hopital's rule yet, i'm in calc ab, the teacher said second semester

Answer 12

also, thank you!

Answer 13

wait, but k is a constanttttt?

Answer 14

9ln(3) - 9 is more accurate, I would keep it in this form unless they explicitly ask for a decimal value.

9ln(3) - 9 *is* a constant. ln(3) has a defined value.

Answer 15

oh

Answer 16

for the limit one I'd have to think a bit on how to prove it w/o L'hopital's rule.