X=e^(t), Y=e^(2t) estimate the parameter to find cartesian equation of curve? sketch the curve and indicate...?
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A) eliminate the parameter to find a Cartesian equation of the curve? B) sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases? x=e^(t) , y=e^(2t) can someone please show me step by step how to do this problem, I'm so lost! please and thank-you
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Answer:
If x = e(t), x² = e(2t) = y; since x > 0 for all t, the cartesian equation is the right branch of y = x². To find the direction, the easiest way is to plug in a few numbers: x(0) = 1, y(0) = 1; x(1) = e, y(1) = e² .... So the arrow is pointing upper-right. Another way is to find the derivative: dy/dx = dy/dt * dt/dx = 2e(2t) / e(t) = 2e(t) which increases as t increases And that's the case in the graph ....
thirteenthgrave at Yahoo! Answers Visit the source
Other answers
If x = e(t), x² = e(2t) = y; since x > 0 for all t, the cartesian equation is the right branch of y = x². To find the direction, the easiest way is to plug in a few numbers: x(0) = 1, y(0) = 1; x(1) = e, y(1) = e² .... So the arrow is pointing upper-right. Another way is to find the derivative: dy/dx = dy/dt * dt/dx = 2e(2t) / e(t) = 2e(t) which increases as t increases And that's the case in the graph ....
thirteen...
Here, we have, x = e^(t) , and, y = e^(2t) = e^t * e^t = x * x SO, y = x^2 >===================< ANSWER
Fazaldin A
Here, we have, x = e^(t) , and, y = e^(2t) = e^t * e^t = x * x SO, y = x^2 >===================< ANSWER
Fazaldin A
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