I need a little help on these questions. If you guys can help thanks a lot! :) Just the answers would be fine. Only 6 questions. 2 in each link. Thanks!
# 1, 2.) http://tinypic.com/view.php?pic=qs7a0p&s=5
# 3, 4.) http://tinypic.com/r/ve135k/5
# 5, 6.) http://tinypic.com/r/219cbpt/5
# 1, 2.) http://tinypic.com/view.php?pic=qs7a0p&s=5
# 3, 4.) http://tinypic.com/r/ve135k/5
# 5, 6.) http://tinypic.com/r/219cbpt/5
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3.) f(x) = (x - 1)/(x + 1)
f(x) = (x + 1 - 2)/(x + 1) = 1 - 2/(x + 1)
f '(x) = 2/(x + 1)²
f '(1) = 2/4 = 1/2
D
4.) Differentiating implicitly:
6x + 2x(dy/dx) + 2y + 2y(dy/dx) = 0
dy/dx = (-2y - 6x)/(2x + 2y)
dy/dx at x = 1 is : -8/4 = -2
A
5.) dy/dx = cos(x)/[2√(4 + sin(x))]
slope of tangent at x = 0: 1/4
Eqn of tangent:
y - 2 = x/4
y = x/4 +2
y(0.12) = 0.03 + 2 = 2.03
B
6.) dr/dt = 0.3 in/sec
dV/dt = 4*pi*r^2 * (dr/dt)
Remember that 4*pi*r^2 is just the surface area of a sphere, so:
dV/dt = (Surface area) * (dr/dt)
dV/dt when Surface area is 100 pi = (100 pi) * (0.3 in/s) = 30 pi in^3/s
A
f(x) = (x + 1 - 2)/(x + 1) = 1 - 2/(x + 1)
f '(x) = 2/(x + 1)²
f '(1) = 2/4 = 1/2
D
4.) Differentiating implicitly:
6x + 2x(dy/dx) + 2y + 2y(dy/dx) = 0
dy/dx = (-2y - 6x)/(2x + 2y)
dy/dx at x = 1 is : -8/4 = -2
A
5.) dy/dx = cos(x)/[2√(4 + sin(x))]
slope of tangent at x = 0: 1/4
Eqn of tangent:
y - 2 = x/4
y = x/4 +2
y(0.12) = 0.03 + 2 = 2.03
B
6.) dr/dt = 0.3 in/sec
dV/dt = 4*pi*r^2 * (dr/dt)
Remember that 4*pi*r^2 is just the surface area of a sphere, so:
dV/dt = (Surface area) * (dr/dt)
dV/dt when Surface area is 100 pi = (100 pi) * (0.3 in/s) = 30 pi in^3/s
A
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1. A
2. C
2. C
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That was pretty awesome