Question

need help on this attachment

Answer 1

just says "which are not one to one"?

Answer 2

yes

Answer 3

or am i looking at the wrong thing? because usually you have some tougher calc problems

Answer 4

lol

Answer 5

make sure the outputs do not repeat. that is all. if they repeat it is not one to one. if they do not repeat it is one to one

Answer 6

f is one to one
g is not because there is a 3 twice
etc

Answer 7

at a quick glance it looks like all are one to one except g
clear?

Answer 8

yeah, can you also help me with one more problem?

Answer 9

lost the site for a moment

Answer 10

that ok

Answer 11

take the derivative term by term.

Answer 12

\[\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^2+1}\]

Answer 13

so
\[\frac{d}{dx}\tan^{-1}(\frac{x}{5})=\frac{1}{5}\times \frac{1}{(\frac{x}{5})^2+1}\] by the chain rule

Answer 14

or course you might want to clean this up a bit

Answer 15

\[\frac{1}{5}\frac{1}{\frac{x^2}{25}+1}\]
\[\frac{5}{x^2+25}\]

Answer 16

damn again

Answer 17

\[\frac{d}{dx}\ln(x)=\frac{1}{x}\] so
\[\frac{d}{dx}\ln(\sqrt{25+x^2})=\frac{1}{\sqrt{25+x^2}}\times \frac{d}{dx}\sqrt{25+x^2}\] by the chain rule again

Answer 18

and
\[\frac{d}{dx}\sqrt{25+x^2}=\frac{1}{2\sqrt{25+x^2}}\times 2x\] again by the chain rule

Answer 19

so finally you get
\[\frac{d}{dx}\ln(\sqrt{25+x^2})=\frac{x}{25+x^2}\]

Answer 20

then add them up (easy since denominators are the same) and you get
\[\frac{5+x}{25+x^2}\]

Answer 21

Ok, so just for practice 2arc(x/3) would be 6squrt(9-x^(2)), right?

Answer 22

is that arcsine?

Answer 23

yes

Answer 24

you would have
\[\frac{1}{\sqrt{1-(\frac{x}{3})^2}}\]

Answer 25

\[\frac{1}{\sqrt{1-\frac{x^2}{9}}}\]

Answer 26

what about the 2 on the outside

Answer 27

this one is a little different because of the square root.

Answer 28

\[\frac{1}{3}\frac{1}{\sqrt{1-\frac{x^2}{9}}}=\frac{1}{3}\frac{1}{\sqrt{\frac{9-x^2}{9}}}\]

Answer 29

the 9 comes outside the radical as a 3, so your "final answer" is
\[\frac{1}{\sqrt{9-x^2}}\] then just multiply by 2

Answer 30

oh crap i made a mistake on the very first line hold on i hope i did not confuse you

Answer 31

\[\frac{1}{\sqrt{1-(\frac{x}{3})^2}}\] should have been
\[\frac{1}{3}\frac{1}{\sqrt{1-(\frac{x}{3})^2}}\] by the chain rule. i forgot the one third out front

Answer 32

you have to multiply by the derivative of
\[\frac{x}{3}\] which is
\[\frac{1}{3}\]

Answer 33

oh ok

Answer 34

so in this case you just get
\[\frac{1}{\sqrt{9-x^2}}\] when you "simplify" it. the two out front just gets multiplied at the end

Answer 35

ok thanks so much

Answer 36

yw