AmTran_Bus
  • AmTran_Bus
Find an equation of the tangent to the curve at the point by first eliminating the parameter
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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AmTran_Bus
  • AmTran_Bus
x=e^t , y=(t-6)^2 ; (1,36)
AmTran_Bus
  • AmTran_Bus
I tried to elem. the parameter and got lnx^2 - 12lnx +36 ?
amistre64
  • amistre64
why would we want to eliminate the parameter? just because it says so?

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AmTran_Bus
  • AmTran_Bus
Correct.
AmTran_Bus
  • AmTran_Bus
Did I even do it right?
amistre64
  • amistre64
ln(x) = t is suitable sure
AmTran_Bus
  • AmTran_Bus
Hum. So what do I do to get the equation? I cant just plug in (1,36) for x and y because ln(1) is 0.
amistre64
  • amistre64
well, since y = (t-6)^2, and t=ln(x) y = (ln(x)-6)^2
amistre64
  • amistre64
in order to make a line, we need a point and a slope ... how do we find the slope?
AmTran_Bus
  • AmTran_Bus
or lnx^2-12lnx+36
amistre64
  • amistre64
no need to expand it ..
AmTran_Bus
  • AmTran_Bus
Hum. Ok. So y-y1=m(x-x1)
amistre64
  • amistre64
good, and we have y1 and x2, we only need m
amistre64
  • amistre64
typos lol
AmTran_Bus
  • AmTran_Bus
So just take delta y/delta x? Which is ... um...
amistre64
  • amistre64
which is chain rule ...
AmTran_Bus
  • AmTran_Bus
Oh. Duh. Gotta take deriv. of that.
amistre64
  • amistre64
yep
AmTran_Bus
  • AmTran_Bus
Give me a sec!
AmTran_Bus
  • AmTran_Bus
2(lnx-6)*1/x
amistre64
  • amistre64
very good, and when x=1? m=?
AmTran_Bus
  • AmTran_Bus
-6?
amistre64
  • amistre64
2(0-6)/1 is not -6
AmTran_Bus
  • AmTran_Bus
It is if you are lazy and plug it in your calc wrong. :)
amistre64
  • amistre64
lol
AmTran_Bus
  • AmTran_Bus
-12
amistre64
  • amistre64
so whats our line?
AmTran_Bus
  • AmTran_Bus
y=-12x+
AmTran_Bus
  • AmTran_Bus
gott get that last number.
amistre64
  • amistre64
y-36 = -12(x-1) is the equation of a line ... but format however you want
AmTran_Bus
  • AmTran_Bus
Okie dokie. So just -12x+1+36? So y=-12x+37?
amistre64
  • amistre64
-12x -12(-1) +36 so no
AmTran_Bus
  • AmTran_Bus
Story of my life. How about -12x+12+36 or y=-12x+48
amistre64
  • amistre64
looking good lol
AmTran_Bus
  • AmTran_Bus
So algebra is harder than calculus. Thank you.
amistre64
  • amistre64
i agree :)

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