help !!
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Find the eqns of the tangent to the curve x²-y²-2xy=4, with a slope of 1...
stuck with this Confused any pros ?
ans : y=x-2 , y=x+2 -
find your dy/dxOriginally posted by vice_edge:Find the eqns of the tangent to the curve x²-y²-2xy=4, with a slope of 1...
stuck with this Confused any pros ?
ans : y=x-2 , y=x+2
you will get
2x - 2y dy/dx - 2x dy/dx - 2y = 0
when slope = 1, dy/dx = 1
hence, you get y=0
sub y=0 back to curve, you get x = 2 or -2
so the 2 pts at which slope = 1 is (2, 0) and (-2, 0)
equation of line with slope 1 and pass through (2, 0)
is y = x-2
equation of line with slope 1 and pass through (-2, 0)
is y = x+2 -
ghee thx engle .. but can u clarify further how to u tackle -2xy ?Originally posted by eagle:find your dy/dx
you will get
2x - 2y dy/dx - 2x dy/dx - 2y = 0
when slope = 1, dy/dx = 1
hence, you get y=0
sub y=0 back to curve, you get x = 2 or -2
so the 2 pts at which slope = 1 is (2, 0) and (-2, 0)
equation of line with slope 1 and pass through (2, 0)
is y = x-2
equation of line with slope 1 and pass through (-2, 0)
is y = x+2 -
d/dx xy can use chain ruleOriginally posted by vice_edge:ghee thx engle .. but can u clarify further how to u tackle -2xy ?
x (dy/dx) + y(1) -
okkk thx alot
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a main entrance of a tall building has a parabolic curve as shown . if arch is 4m wide at the bottom and 3m high , find the area of this main entrance .. help !!
i stuck at the indefinite integral part... ans is 8 metre square
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Since curve is a parablioc curve, it is highly likely the curve is trig function.Originally posted by vice_edge:
a main entrance of a tall building has a parabolic curve as shown . if arch is 4m wide at the bottom and 3m high , find the area of this main entrance .. help !!
i stuck at the indefinite integral part... ans is 8 metre square
Assume that I take the left edge of the curve to be the origin, the curve will be a sine curve.
Amplitude of curve = 3. This implies that there is coefficient of 3 in the sine function.
Let y = f(x)
f(0) = 0
f(2) = 3
f(4) = 0
Recall that sin 0 = 0, sin (pi) = 0, pi is the next value of 0.
For this situation, 4 is the next value of 0.
Therefore, imagine sin (pi) = 0
Sin(pix 4/4) = 0
Sin(pi/4 x 4) = 0
When x = 4, y = 0
Hypothesis: y = 3 sin [(pi/4) x]
To confirm, check with f(2) = 3 and f(0) = 0
After it has been confirmed, the parabolic curve has the eqn y = 3 sin [(pi/4) x]
Integrate it from 0 to 4 since I have taken the left edge of the curve to be the origin.
u will get
[-12/pi cos(pi/4) x ] from 0 to 4.
Area of the curve = 24/pi
= 7.639 = 7.64 m^2