Question: Sketch the region in the plane consisting
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.
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> Use a graphing device to graph the polar curve. Choose the parameter interval carefully to make sure that you produce an appropriate curve. r = cos(0/2) + cos(0/3)
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> The graph of f is shown. (a). Explain why the series is not the Taylor series of f centered at 1. (b). Explain why the series is not the Taylor series of f centered at 2. yA f 1+ 1 1.6 – 0.8(x – 1) + 0.4(x – 1) – 0.1(x – 1)3 + · .. 2.8 + 0.5(x –
> Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. 0<r< 4, -m/2 s0 < m/6 -1/2 < 0 < T/6
> Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. r> 0, 7/3 s0 < 27/3
> Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. 1srs2
> The Cartesian coordinates of a point are given. (i). Find polar coordinates (r, θ) of the point, where r > 0 and r (ii). Find polar coordinates (r, θ) of the point, where r (a) (3,/3, 3) (b) (1, –2)
> The Cartesian coordinates of a point are given. (i). Find polar coordinates (r, θ) of the point, where r > 0 and r (ii). Find polar coordinates (r, θ) of the point, where r (а) (2, —2) (b) (-1, 3)
> Sketch the curve with the given polar equation. r2θ = 1
> Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point. (a) (-/2, 57/4) (b) (1, 57/2) (c) (2, –77/6)
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> Use a graphing device to graph the polar curve. Choose the parameter interval carefully to make sure that you produce an appropriate curve. r= 2 – 5 sin(6/6)
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> Sketch the curve with the given polar equation. r = 3 cos 6θ
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> Sketch the curve with the given polar equation. r = 4 sin 3θ
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> Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point. (а) (1, п) ъ) (2, -2т/3) (с) (-2, 3п/4)
> Sketch the curve with the given polar equation. r = θ, θ > 0
> Use a graphing device to graph the polar curve. Choose the parameter interval carefully to make sure that you produce an appropriate curve. r = | tan e |lcot el (valentine curve)
> Sketch the curve with the given polar equation. r = sin θ
> Sketch the curve with the given polar equation. r2 – 3r + 2 = 0
> Sketch the curve with the given polar equation. θ = -π/6
> For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a). A circle with radius 5 and center (2, 2) (b). A circle centered at the origin with ra
> For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a). A line through the origin that makes an angle of π/6 with the positive x-axis (b). A
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> Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r (а) (1, 7п/4) (b) (-3, п/6) (с) (1, — 1)
> Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 2cx
> Find a polar equation for the curve represented by the given Cartesian equation. x + y = 9
> Find a polar equation for the curve represented by the given Cartesian equation. x = -y2
> Use a graphing device to graph the polar curve. Choose the parameter interval carefully to make sure that you produce an appropriate curve. r= esin e – 2 cos(40) (butterfly curve)
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> Identify the curve by finding a Cartesian equation for the curve. r = csc e
> Identify the curve by finding a Cartesian equation for the curve. r= 2 sin e + 2 cos e
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> Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. 2 <r< 3, 57/3 < 0 < 7m/3
> Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r (а) (2, т/3) (b) (1, — Зӕ/4) (с) (-1, п/2)
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> Solve the inequality in terms of intervals and illustrate the solution set on the real number line. x2 < 3
> Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients. (a) (r' + x)(x? – x + 3) 1 (b) x° - x .3
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> Sketch the region bounded by the curves. x + 4y = 8 and x = 2y2 - 8
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