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wouldn't e^2x/2 get cancelled when we take ln?
You can simplify this further.The question was dy/dx=e^(2x+y) right?
dy/dx=e(2x+y)
dy/dx=e^(2x) x e^( y )
[1/e^( y )] dy = e^(2x) dx
e^(-y) dy = e^(2x) dx
Integrate both the sides.
-e^(-y) = [e^(2x)/2] + c
Put x=0 and y=0 to find the value of 'c'.
-e^(-y) = [e^(2x)/2] + c
-e^(-0) = [e^(0)/2] + c
-1 = (1/2) + c
-1 - (1/2) = c
-3/2 = c
Put back this value of 'c' in the integrated solution.
-e^(-y) = [e^(2x)/2] + c
-e^(-y) = [e^(2x)/2] - (3/2)
Multiply the equation by a '-' sign.
- {-e^(-y) = [e^(2x)/2] - (3/2)}
e^(-y) = (3/2) - [e^(2x)/2]
Put 'ln' on both the sides.
ln e^(-y) = ln {(3/2) - [e^(2x)/2]}
-y = ln {(3/2) - [e^(2x)/2]}
y = - ln {(3/2) - [e^(2x)/2]}
Therefore, the answer was 'y = - ln {(3/2) - [e^(2x)/2]}'.
yes mine was also 1/2 but what was the method you appliedI got 1-x+1/2x^2 and I'm pretty sure it's correct. I will have all the correct answers in about 2 hours though
You can simplify this further.
Final answer : y = ln(2/(3-e^2x))
Did you do the parts of the questions in order? As long as you did that, I think you should be OK.guys what will happen if idid not arranged the answer sheet in order but i have written the questions numbers on the side some one pls? pls help so
yaDid you do the parts of the questions in order? As long as you did that, I think you should be OK.
well almost everyone in my school got (pi/4)(e^2 - 1). I am very confident that's the correct answer for the volume.Yaar according to some toppers and me the only answer to volume question was 1 by 4 pi e^2
yes u r right bro. there were definitely 3 stationary points. pi/2, pi/12, 5pi/12.uhm weren't there 3 stationary points in q 6, as in pie/2, pie/12 and 5pie/12?
there were 3 dear brother. and the point was a maxima, not a minima!No, there were two and the point was minimum point, according to what i solved.
I think due to range bcoz range was less not 360,
though i dont exactly remember!
yeah and there were 3 stationary points! XD pi/2 was one of them!!!I have the exam paper infront of me right now, it says 0 < x < pi
i guess u need to check again! the answer clearly is 1 - x + (1/2) x^2i got the ans= 1-x+1/4x^2
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