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anonymous
 5 years ago
For y=(1/2)xsinx where 0<x<3pi
How do I get the Domain, Horizontal Asymptotes, Vertical Asymptotes, Slant asymptotes, x and y intercepts, increasing and decreasing intervals, as well the concativity and inflection points. How do you get all of that in cases like this one where the equation is trigonometric?
anonymous
 5 years ago
For y=(1/2)xsinx where 0<x<3pi How do I get the Domain, Horizontal Asymptotes, Vertical Asymptotes, Slant asymptotes, x and y intercepts, increasing and decreasing intervals, as well the concativity and inflection points. How do you get all of that in cases like this one where the equation is trigonometric?

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Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0To find the domain, all you care about is 1), is the denominator = 0 ? 2), is the number inside a square root negative ?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0in your case, x/2 is a polynomial and sin(x) is a trig function with no vertical asymptotes, so the denominator is never 0 and we don't have to worry about imaginary numbers.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0trig functions oscilate, so there is no need to consider about horizontal asymptotes.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0for the same reason, slant asymptotes will not be there

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1For domain it is provided, 0<x<3pi For vertical asymptotes look for xvalues within domain that make y undefined, in this case y is defined on all of x Horizontal asymptotes can be obtained by looking at the limit of function as x>infinity, but in this case with a trig function there is no limit because its cyclical. xintercept, set y=0 sinx = 1/2x

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0vertical asymptotes are the points where your function has a denominator equal to zero, but not the numerator. again, since there were not problem with the domain we don't have to worry about that.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0for the xint, solve for x when y=0 for the yint, solve for y when x=0.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0to see whether f is increasing or decreasing, you will find the derivative of your function f. if f'>0, then the function is increasing. the opposite would work similarly.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0to see whether f is concave up or down, you will find the second derivative of your function f. if f">0, then it is concave up. the opposite is similar.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0let me know if you need more help.
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