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Question
A curve has equation y= sinx/x x>0. All turning points of satisfy
a) xsinx - cosx = 0
b)xcosx + sinx = 0
c) x-tanx = 0
d) xsinxcosx = 0
Hi Kristin
Just solve for x in each of those equations.
a. xsinx - cosx = 0
so xsinx = cosx
so x = cotx. You can solve this equation by graphing them both.
b. xcosx + sinx = 0
so x = -tanx. You can solve this one by graphing as well
c. x - tanx = 0
so x = tanx You can solve this by graphing
d. Either x = 0 or sinx = 0 or cosx = 0 so x = 0,npi,pi/2 + npi
where pi = 3.1415...
I hope this helps,
Robi
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Answers by Expert:
Robi Bhattacharjee
Expertise
I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.
Experience
I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).
Organizations
I am in the San Diego Math Circle
Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.
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