Question

Multiple choice question

Answer 1

I believe it's B (f''(0) one). because when you take derivative of this series twice, there still will be all terms with x, so f''(0) should be 0, not 3/2

Answer 2

The other ones are probably right though?

Answer 3

Like true I mean

Answer 4

It would be 3 wouldn't it? For B

Answer 5

yeah. only one is false :)

Answer 6

Not 3/2. Ok that makes sense

Answer 7

it shouldn't be 3, supposed to be 0 because all terms contain x. no constant

Answer 8

There's a 3 there for some reason

Answer 9

oops! im wrong.

Answer 10

sorry, i though all exponents are even...

Answer 11

but that's still the right answer? :)

Answer 12

sorry, yeah, it's still wrong. should be 3.

Answer 13

\(\dfrac{d^2}{dx^2} \dfrac{3x^2}{2!} = \dfrac{3\cdot 2}{2} = \boxed{3}\)

Answer 14

yeah it's still B

Answer 15

sorry i messed up lol

Answer 16

wait why did you plug in 2 for x

Answer 17

i didn't . derivative of x^2 is 2x, so that where 2 came from.

Answer 18

Oh wait nevermind

Answer 19

I got it now. thanks :)

Answer 20

ok glad i helped

Answer 21

How could we rule out A?

Answer 22

I'm not sure, I think when you add and subtract in that pattern it ends up being -2/3 for x?

Answer 23

it does, but the alternating signs had me thinking :)

Answer 24

great question, this series looks familiar, i cant put my finger on what function it is...
we didnt rule out A, we just ignored it

Answer 25

\[1+x+x+x^2+x^3+...=3\]
\[\frac{1}{1-x}=3\]
\[\frac{1}{3}=1-x\]
\[\frac{1-3}{3}=-x\]
\[-\frac{2}{3}=-x\]
hmm,

Answer 26

i was thinking that if x<0, then the odd degrees go negative and fits the pattern; was hoping to see it pan out; but might be some caveat of x>0 for this to work

Answer 27

\[1-x+x^2-x^3+x^4-...=3\]
\[(1+x^2+x^4+...)-(x+x^3+x^5+...)=3\]
\[(1+x^2+x^4+...)-x(1+x^2+x^4+...)=3\]
\[(1-x)\sum_{n=0}^{\infty} (x^{2})^{n}=3\]
\[\frac{1}{1-x^2}=\frac{3}{1-x}\]
\[\frac{1}{3}=\frac{1-x^2}{1-x}\]
\[\frac{1}{3}=\frac{(1-x)(1+x)}{1-x}\]
\[\frac{1}{3}=1+x\]
\[\frac{1}{3}-1=x=-\frac23\]

Answer 28

lol, that was fun

Answer 29

Ah okay well thanks for that :) I was wondering why that one was true too

Answer 30

:) i like the joker animated gif from the dark knight ... when hes sitting in the police holding cell

Answer 31

haha yeah this