Question

Turing and other geniuses!

Answer 1

am i a genius?

Answer 2

i d k.. u should know about u . ;)

Answer 3

i am one...:) oo limits huh?

Answer 4

The limit from the left at x=0.2
from the graph you can see that if you go along the graph, from the left side, you approach y=2.6 at x=0.2
so \[\lim_{x \rightarrow 0.2^-}C(x)=2.6\]the other symbol with the plus sign means the same thing, but from the right...

Answer 5

option?

Answer 6

fill in the box with 2.6 it looks like, the other thing is just if the limit doesn't exist....

Answer 7

there are 4 options! :O

Answer 8

the next one as I said is from the right. Looking at the graph we can see that\[\lim_{x \rightarrow 0.2^+}C(x)=3\]...

Answer 9

ohh, u mean A?

Answer 10

there can't be two answers.. :/

Answer 11

Saif, where do you get these practice questions from?

Answer 12

Internet. :P

Answer 13

The final bit asks you to find the actual limit. There is a theorem that states that \[\lim_{x \rightarrow a}C(x)\]exists at a if and only if\[\lim_{x \rightarrow a^+}C(x)=\lim_{x \rightarrow a^-}C(x)\]here we can see that this is not the case, the right and left-had limits are different, so \[\lim_{x \rightarrow 0.2}C(x)\]does not exist :)

Answer 14

1. 2.6

2. 3

3. does not exist

Answer 15

Dude, Basic net, No exact location??

Answer 16

server's getting jumpy ion me...

Answer 17

for the explanation of the third one the left hand limit doesnt match the right hand limit so in turn the limit doesnt exist

Answer 18

we cannot make all of them!!

Answer 19

oh sorry turning test i didnt see u reply

Answer 20

wait we can.

Answer 21

make what saifoo?

Answer 22

Where do you see four options? I see six slots for three questions.

Answer 23

yea right

Answer 24

Thanks!! =D

Answer 25

how about this one?

Answer 26

is it a dot at x=3?? i mean is that it has no value at 3?

Answer 27

looks like
a)2
b)undefined
c)... I want to say yes, let me check...

Answer 28

nope

Answer 29

2
undefined
no

Answer 30

as it is discontinuos turning point the function doesnt have any value

Answer 31

so no?

Answer 32

I still say yes after looking it up, look here's the theorem
http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx

Answer 33

yes it is a NO

Answer 34

lol.

Answer 35

let's toss a coin.

Answer 36

because the limit at that point exists and is 3 it follows the theorem, can you provide a counter-argument Akshay?

Answer 37

Finally .

The function is not continuous at this point. This kind of discontinuity is called a removable discontinuity. Removable discontinuities are those where there is a hole in the graph as there is in this case. is what it says point

Answer 38

everything's going over my head. :o

Answer 39

yes akshay is right, it is removable but still counts
I agree now :)
c)no

Answer 40

KICKING

Answer 41

u kicked me:o o.0

Answer 42

who, what?

Answer 43

weird question!!

Answer 44

Oh I made master!

Answer 45

what a mod, who kicks peepl for the fun of it! :(

Answer 46

lol, u said me to do it.

Answer 47

where

Answer 48

pffft!

Answer 49

i know u deleted that.

Answer 50

No.

Answer 51

C

Answer 52

both the values come out to be 9

Answer 53

u ca delete stuff>?

Answer 54

quick one..

Answer 55

I forgot how to do these :(
I bet akshay's right though

Answer 56

np ty guys! =)

Answer 57

D

Answer 58

f(x)=6x^2+5
g(x)=1/sqrt x^2

Answer 59

sorry got em backwards

Answer 60

can i ask how?

Answer 61

yup

Answer 62

How?

Answer 63

see f(gx) is like when u put g(x) instead of x in the function f(x).. i hope that self explains itself?

Answer 64

Damn! im sleeping.. lol.

Answer 65

Oh just look at the functions
\[g(x)=6x^2+5\]\[f(x)={1\over \sqrt {x^2}}\]exactly plug in f[g(x)]

Answer 66

just want to make sure, we have to double diff it to get the stat points?

Answer 67

double differentiating and setting to zero gets the inflection points, I don't know about stat points...

Answer 68

stationary points.

Answer 69

stat points r same as infletion points i believe

Answer 70

hmm, im getting 10.

Answer 71

so y = 10?

Answer 72

that shud be fine we trust ur differentiation saifoo :P

Answer 73

i mean the equation?

Answer 74

probably
this one is just finding where the first derivative is undefined
10x-2=0
x=5

Answer 75

so it....? o_O

Answer 76

10

Answer 77

double differentiate, you get y=10

Answer 78

the question ask about horizontal tangent, not inflection points :/

Answer 79

wait it says the point at which... so it need the points right?

Answer 80

OmG! sorry im sleeping. :O
it's 07:55am here.

Answer 81

The point is where f'(x)=0=10x-2
x=5
f(5)=5(25)-2(5)-2=113

Answer 82

o.O

Answer 83

Gn safioo rather GM :P

Answer 84

im confused. :/

Answer 85

\[x\ne5\]

Answer 86

oh man I messed up
f(5)=f(5)=5(25)-2(5)+3=118

Answer 87

Zarkon!!!!!!!! you look cool in your real pic!! :P

Answer 88

\[x=\frac{1}{5}\]

Answer 89

ty

Answer 90

how u got that? o_O

Answer 91

that's what I get for trying to do this over dinner :/
by solving what I wrote
5x-2=0

Answer 92

soorry stiill cant' type
10x-2=0

Answer 93

LOL.

Answer 94

yeah told you...

Answer 95

anyway get f(1/5) I know you can do that in your sleep