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sam0004
 11 months ago
Lim as x approaches pi/6 of (sin(x)sin(pi/6))/xpi/6
sam0004
 11 months ago
Lim as x approaches pi/6 of (sin(x)sin(pi/6))/xpi/6

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myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1compare to definition of derivative

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1\[\lim_{x \rightarrow a}\frac{f(x)f(a)}{xa}=f'(a)\]

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0So the limit would = 1?

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1what is f(x) and what is a?

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0F(x)=sin(x), f(a)=sin(pi/6)

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1:( if f=sin(x), then f'=?

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1right now plug in a to get your answer

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1\[\lim_{x \rightarrow a}\frac{f(x)f(a)}{xa}=f'(a) \text{ or we could say it equals } =(f(x))'_{x=a}\]

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1\[\lim_{x \rightarrow \frac{\pi}{6}}\frac{\sin(x)\sin(\frac{\pi}{6})}{x\frac{\pi}{6}}=(\sin(x))'_{x=\frac{\pi}{6}} \]

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1do you see all i'm trying to get you to do is use the definition of derivative

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1you are suppose to determine f and a then find f' then plug a into f' to get the result you are searching for

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0Any chance you can help with critical numbers?

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0I know i need the derivative

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1do you mean 4x/(x^2+1)? Also what did you get for the derivative?

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0Yes. F'(x)=(4x^2+4)/(x^2+1)^2

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1thats great now find when F'=0 Also we don't have to worry when F' DNE because x^2+1 is always positive. so F'=0 when top=0 so when 4x^2+4=0 solve for x now

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1I think you should retry solving 4x^2+4=0 I will give you a (you will get two real solutions)

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1right sqrt(1)=1 so x=1 or x=1

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1those are the critical numbers for F.

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0Find the intervals where f(x)=4/(x^+1) is increasing or decreasing.

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1is that f(x)=4/(x+1)? like you weren't trying to write an exponent right?

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0I Find the derivative...then set the denominator equal to zero...put those numbers on a number line and plug in numbers to find the intervals?

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0I was writing an exponent

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0I apologize for missing the exponent

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0It should have said 4/(x^2+1)

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1well I don't know what f you are looking at exactly. but yeah you definitely need to find f' because f' tells you if f is decreasing or increasing or neither f'=0 means the function is resting f'>0 means f is increasing f'<0 means f is decreasing I first find when f' =0 and when f' does not exist and then test each interval around those numbers to see if the function is increasing there or decreasing there

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1so what is f' first?

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1(x^2+1)^2 does not equal x^4+1

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1just leave is at (x^2+1)^2

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0Increasing from negative infinity to 0 and decreasing from 0 to positive infinity

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1also x^2+1 is always positive so f' and f exist everywhere so you just need to find when f'=0 which is when 8x=0 which is when x=?

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0F(x)=3x^212x=5 over the closed interval 0,3. Find absolute extrema.

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0Do i again begin with taking the derivative?

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1see if there any critical numbers between 0 and 3 first

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1which means you need to find f' which all means you need find when f'=0 this looks like you meant to write a polynomial so we don't need to worry when f' dne

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1ok do F(0) and F(2) and F(3) which ever one of these are the lowest value is the absolute min value which ever one of these are the highest value is the absolute max value

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0Ok so you use the tow numbers in the interval and the critical number?

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1also I don't know what your function is exactly critical numbers in between the critical numbers and any included endpoints just plug them back into the original function

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1you have two equal signs

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1i'm guessing that second equal sign is a + or a 

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1can't decide which one

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1ok do you want me to check your answers for this one or are you just going through problems and getting ideas on how to do them so you can pass your final

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1like it seems like you are studying

sam0004
 11 months ago
Best ResponseYou've already chosen the best response.0I just need ideas on how to pass my final...i struggle with a few areas.

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1i would like to help you more but...

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1I have to go do some house stuff good luck on your final

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1i hope i was helpful
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