MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 3 2, 5 2 C) - 5 2

Transcription

1 Test Review (chap 0) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) Find the point on the curve x = sin t, y = cos t, - π t π, closest to the point, 0. (Hint: ) Minimize the square of the distance as a function of t.) A) (, 0) B) (-, 0) C), D), Find an equation for the line tangent to the curve at the point defined by the given value of t. ) x = csc t, y = cot t, t = π ) A) y = -x + B) y = x + 7 C) y = x - D) y = 7 x - Find the value of d y/dx at the point defined by the given value of t. ) x = tan t, y = sec t, t = π ) A) B) - C) - D) Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the curve x = f(t), y = g(t) at the given value of t. ) x - t - t = 0, ty + t =, t = ) A) - B) - C) D) - Find the area. ) Find the area of the region between the curve x = e 6t, y = 6 e-t and the x-axis, 0 t ln 9. ) A) 6 B) C) 8 D) 9 Find the length of the curve. 6) x = sin t, y = cos t, 0 t π A) 9 B) C) 6 D) 8 6) 7) x = (t + 7) /, y = 7t, 0 t 7) A) B) C) D) Plot the point whose polar coordinates are given.

2 8) (-, π/) 8) - - A) B) C) D) Find the Cartesian coordinates of the given point. 9) (, π/6) 9) A), B), C), D), 0) (-6, 0) A) (-6, 0) B) (6, 0) C) (0, -6) D) (0, 6) 0)

3 Graph the set of points whose polar coordinates satisfy the given equation or inequality. ) 0 θ π, r ) A) B) C) D) Find the polar coordinates, 0 θ < π and r 0, of the point given in Cartesian coordinates. ) (, - ) ) A), 7π B), π C), 7π D) (, π ) (-, 0) ) A) (-, π) B) (, π) C), π D), π

4 Find all the polar coordinates of the point. ) (-, π/) A) (, π/ + nπ), (, π/ + nπ) B) (, π/ + nπ), (-, -π/ + nπ) C) (, π/ + nπ), (-, π/ + nπ) D) (, π/ + nπ), (-, π/ + nπ) ) Determine if the given polar coordinates represent the same point. ) (r, θ), (-r, θ + π) A) Yes B) No ) Find the area of the surface generated by revolving the curves about the indicated axis. 6) x = t +, y = t + t, - t ; y-axis 6) A) 68 π B) π C) 8π D) π Determine if the given polar coordinates represent the same point. 7) (, π/), (-, -π/) A) Yes B) No 7) Parametric equations and and a parameter interval for the motion of a particle in the xy -plane are given. Identify the particleʹs path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. 8) x = cos t, y = sin t, π t π 8) y x

5 A) x + y = ; Counterclockwise from (, 0) to (, 0), one rotation y x B) x + y = ; Clockwise from (, 0) to (, 0), one rotation y x C) x + y = ; Counterclockwise from (-, 0) to (, 0) y x

6 D) x + y = ; Clockwise from (, 0) to (-, 0) y x 6

7 Graph the set of points whose polar coordinates satisfy the given equation or inequality. 9) r 9) A) B) C) D) 7

8 0) π θ π, r = - 0) A) B) C) D) Describe the graph of the polar equation. ) r = r cos θ A) Horizontal line passing through (0, ) B) Circle of radius and center (0, ) C) Circle of radius and center (, 0) D) Vertical line passing through (, 0) ) Replace the polar equation with an equivalent Cartesian equation. ) r = 7 cot θ csc θ A) y = 7 x B) y = 7x C) y = 7x D) y = 7x ) 8

9 Replace the Cartesian equation with an equivalent polar equation. ) x + y - x = 0 A) r = sin θ B) r cosθ = sin θ C) r sinθ = cos θ D) r = cos θ ) Find the area of the specified region. ) Shared by the circles r = cos θ and r = sin θ A) ( - ) B) (π - ) C) (π - ) D) π ) Replace the Cartesian equation with an equivalent polar equation. ) xy = A) r sin θ cos θ = B) r sin θ = C) r sin θ cos θ = D) rsin θ = ) Find the length of the curve. 6) The spiral r = e θ, 0 θ π A) 0 (e0π - ) B) 0 (π - ) C) e 0π - D) 6 (eπ - ) 6) Replace the polar equation with an equivalent Cartesian equation. 7) r = r cos θ A) x = B) x + (y - 7) = 89 C) (x - 7) + y = 89 D) (x - 7) + y = 0 7) Find the area of the specified region. 8) Inside the smaller loop of the limacon r = + 0 sin θ A) π B) ( - π) C) π D) (π - ) 8) Find the slope of the polar curve at the indicated point. 9) r = cos θ, θ = π 9) A) B) - C) D) - 0) r = -9 csc θ, θ = π 0) A) B) - C) 0 D) Undefined 9

10 Find the length of the curve. ) The parabolic segment r = + cos θ, 0 θ π A) π B) ( - ln( - )) C) 6 D) ( + ln( + )) ) Describe the graph of the polar equation. ) r cos θ + r sin θ = A) Vertical line passing through (, 0) B) Parabola with vertex (, ) opening upward C) Line with slope - and y-intercept (0, ) D) Line with slope and y-intercept (0, ) ) 0

11 Answer Key Testname: TEST-CH0-REVIEW ) D ) C ) B ) D ) C 6) A 7) C 8) B 9) B 0) A ) B ) C ) B ) D ) A 6) C 7) B 8) C 9) D 0) A ) C ) D ) D ) C ) B 6) D 7) C 8) D 9) B 0) C ) D ) C