Question

I need AP Calculus help!!

Answer 1

i will post the assignment soon!

Answer 2

Help with all plz!

Answer 3

hi

Answer 4

the circled questions btw

Answer 5

for the first one, its just 8 thats posted?

Answer 6

i mean circled

Answer 7

its numbers 10, 14, 16, 18, 22

Answer 8

oh i was looking at the first one

Answer 9

kk

Answer 10

oh man, that second one's really hard to read lol so lets do the first one

Answer 11

kk

Answer 12

k so for 8 what is x approaching? i cant see

Answer 13

we dont have to do number 8 lol

Answer 14

:\ it looked circled to me lol

Answer 15

its only numbers 10, 14, 16, 18, 22

Answer 16

do you not have to do the problem in your first attachment?

Answer 17

oh yeah duh i forgot i do lolz

Answer 18

haha ok cool well i basically cant read any of them cuz they're blurry so can you just type out one that you need help with?

Answer 19

kk

Answer 20

hang on

Answer 21

number 8 its as x goes to infinity

Answer 22

so it's as x-> infinity of (2x^2)/(x^2 +3) ? is that right?

Answer 23

2x^5/ x^5+3

Answer 24

oh ok.

Answer 25

have y'all talked about L'Hospital's Rule yet?

Answer 26

i dont think so

Answer 27

k.

Answer 28

what is the L'hospitals rule? can u plz explain

Answer 29

i don't think you're supposed to use it if you haven't covered it yet. you don't need it anyway.

Answer 30

so you start by considering the terms with the highest exponents

Answer 31

if I remember correctly, since x is approaching infinity and it's a rational function, you can rewrite it only including the x's with the greatest exponents

Answer 32

so what would you have if you did that?

Answer 33

hang on im kinda confused

Answer 34

that's ok. so what i'm saying is your next step is to rewrite the limit excluding the +3 in the denominator

Answer 35

to exclude the +3 in the denominator how do u do tht?

Answer 36

you can do this because when x goes to infinity, 2x^5 and x^5 approach infinity and the 3 basically doesn't change the fraction anymore

Answer 37

because if you imagine really high numbers, say x=100, x^5 would be 10000000000 and 2x^5 would be 20000000000 and the +3 in the denominator makes less and less of a difference in the fraction. (10000000000/20000000003 is really close to 10000000000/20000000000)

Answer 38

oh ok

Answer 39

in other words, the fraction approaches 1/2

Answer 40

im sorry, it approaches 2

Answer 41

because 2x^5 is in the numerator

Answer 42

oh ok so ur limit is basically 2 then right?

Answer 43

yup

Answer 44

oh ok now i get number 8

Answer 45

so in questions like that, where x is approaching infinity, you can disregard any terms that arent the variables with the highest exponent. like if you had an x^4 being added/subtracted somewhere in the fraction, you could disregard that, too.

Answer 46

why can u?

Answer 47

for the same reason, because as x approaches infinity, they change the fraction less and less, even though it has x in it....those terms approach infinity slower than terms of higher powers.

Answer 48

im kinda confused on tht part

Answer 49

it's kind of counter-intuitive at first

Answer 50

oh ok

Answer 51

as x gets greater, the difference between x^5 and x^4 also gets greater. if x is 10, then x^5 is 100000 and x^4 is 10000, x^5 is 10 times greater than x^4. but when x= 100, x^5 becomes 100 times bigger than x^4, and so on, until x^5 is infinitely bigger than x^4 and you can disregard x^4.

Answer 52

oh ok now i get it

Answer 53

:) cool

Answer 54

can u help me with the continuity limits and one-sided ones those ones are the ones that r confusing

Answer 55

i can help w one more then i need to get my own work done haha

Answer 56

kk

Answer 57

so i guess pick one for us to do

Answer 58

kk

Answer 59

i think i get the rest on my THQ but i need help with the continuity ones

Answer 60

k

Answer 61

let me post the problem

Answer 62

kk

Answer 63

\[\lim_{x \rightarrow 4-} \frac{ \sqrt{x}-2 }{ x-4 } \]

Answer 64

so first notice that when x = 4, f(x) = 0/0, which is undefined.

Answer 65

yeah

Answer 66

and since x is approaching 4 from the left (less than 4, getting greater) both the numerator and denominator are going to be negative...do u get that?

Answer 67

can u explain it a bit more im still a bit confused

Answer 68

sure. so the way i think of it, is to basically imagine x as some number a little less than 4.. 3.something. when you plug that number into the denominator, 3.something - 4 is always going to be negative. (anything less than 4) - 4 will be negative, right? (3-4=-1, 3.5-4=-0.5, 3.99-4 = -0.01)

Answer 69

oh yeah so its like it keeps on approaching 4 right?

Answer 70

and for the numerator, you can imagine that since the square root of 4 is 2, the square root of anything less than 4 will be less than 2... when you subtract 2 from that number, the result is negative

Answer 71

ya it keeps approaching 4

Answer 72

but from the less-than-4 side because it has the minus sign (x->4-)

Answer 73

basically the limit for it will negative right?

Answer 74

well the numerator and denominator are both negative, right?

Answer 75

so the fraction comes out positive

Answer 76

oh ok

Answer 77

why r limits soo confusing :3

Answer 78

lol i know. wanna see my limit problem that no one will answer?

Answer 79

Limit as x->(pi/2) of [tanx+1/(x-pi/2)]?

Answer 80

thats my question that no one will answer :(

Answer 81

i had it on a quiz today

Answer 82

can u do the substitution method for tht one

Answer 83

i think

Answer 84

idk

Answer 85

no because tan of pi/2 is undefined, it goes to neg infinity and infinity from the right and left....

Answer 86

oh yeah ur right oops lol

Answer 87

ya...it's brutal.

Answer 88

anyway

Answer 89

but im still kinda confused on the continuity limits and one-sided ones

Answer 90

oh boy satellite's here.... it's about to get real xD

Answer 91

i just realized that your problem is tricky. you need to factor your x-4 into (sqrt(x)-2)(sqrt(x)+2) then cancel out the numerator

Answer 92

\[\lim_{ x\to\frac{\pi}{2}}\frac{\tan(x)+1}{x-\frac{\pi}{2}}\]?

Answer 93

oooh well that's my problem but not hers

Answer 94

mines posted

Answer 95

oh ok

Answer 96

somewhere down the list!