| № |
Condition |
free/or 0.5$ |
| m53859 | Find f (x). Compare the graphs of f and f and use them to explain why your answer is reasonable.
F(x) = x4 - 2x3 + x2 |
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| m53860 | Find f (x) If it is known that
d/dx [f(2x)] = x2 |
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| m53861 | Find h In terms of f and g .
(a) h(x) = f(x) g(x)/f(x) + g(x)
(b) h(x) = f(g (sin 4x) |
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| m53864 | Find limx→∞ f(x) if, for all x > 1, |
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| m53867 | Find numbers a and b such that √ax + b - 2/ x = 1. |
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| m53868 | Find parametric equations for the path of a particle that moves along the circle x2 + (y - 1)2 = 4in the manner described.
(a) Once around clockwise, starting at (2,1)
(b) Three times around counterclockwise, starting at (2,1)
(c) Halfway around counterclockwise, starting at (0,3) |
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| m53869 | Find points P and Q on the parabola y = 1 - x2 so that the triangle ABC formed by the x-axis and the tangent lines at P and Q is an equilateral triangle. (See the figure.) |
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| m53870 | Find R (0), where
R(x) = x - 3x3 + 5x5 / 1 + 3x3 + 6x6 + 9x9 |
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| m53871 | Find the 50th derivative of y = cos 2x. |
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| m53872 | Find the absolute maximum and absolute minimum values of f on the given interval.
(a) f(x) = 12 + 4x - x2, [0, 5]
(b) f(x) = 2x3 - 3x2 - 12x + 1, [-2, 3]
(c) f(x) = x3 - 6x2 + 5, [-3, 5] |
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| m53874 | Find the approximations Ln, Rn, Tn, and Mn for n = 5, 10, and 20. Then compute the corresponding errors EL, ER, ET, and EM. (Round your answers to six decimal places you may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when is doubled? |
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| m53875 | Find the approximations Tn, Mn, and Sn for n = 6 and 12. Then compute the corresponding errors ET, EM and ES. (Round your answers to six decimal places you may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when n is doubled? |
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| m53878 | Find the arc length function for the curve with y = 2 x3/2 starting point Po (1,2) . |
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| m53879 | Find the arc length function for the curve y = sin-1 x + √(1 - x2) with starting point (0, 1). |
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| m53880 | Find the area bounded by the curves y = cox x and y = cos2x between x = 0 and x = π. |
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| m53881 | Find the area enclosed by the curve r2 = 9 cos 5( ? |
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| m53882 | Find the area enclosed by the x-axis and the curve
x = 1 + et, y = t - t2 |
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| m53883 | Find the area inside the larger loop and outside the smaller loop of the limaçon r = 1/2 + cos θ. |
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| m53884 | Find the area of the crescent-shaped region bounded by arcs of circles with radii r and R. (See the figure.) |
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| m53885 | Find the area of the region bounded by the given curves.
(a) y = x2, y = 4x - x2
(b) y = 1 - 2x2, y = |x|
(c) y = sin(πx/2), y = x2 - 2x |
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