W AutoSave Off H 2 MAT 291 (SUPPL EXAM,JAN 2011) - Compatibility Mode Saved File Home Insert Draw Design Layout References (b) Search CK Mailings Review View Help Find the radius of curvature and the centre of curvature of the curve: Comments Editing at the point (12) (15) QUESTION 3: (a) The motion of a particle performing damped vibrations is given by y = e¹ sin 2t, (b) (c) Page 2 of 3 381 words English (United States) Text Predictions: On y being the displacement from its mean position at time t. Show that y is a 1 maximum when t=- tan (2) and determine this maximum displacement to three significant figures. Find the range of values of x for which the following series is convergent: (x-2), (x-2)(x-2)³ (x-2)" +...+ +... 1 2 3 n By the use of Maclaurin's series, obtain the expansion of sin including the term x³. Accessibility: Unavailable (10) (10) -1 x, up to and (5) 2 Share Focus + 100% W AutoSave Off ひ MAT 291 (SUPPL EXAM,JAN 2011) - Compatibility Mode Saved . Search File Home Insert Draw Design Layout References Mailings Review View Help QUESTION 4: (a) Suppose V a²v a²v a²v Simplify (10) (b) The base radius of a cone, 7, is decreasing at the rate of 0.1 cm/s while the perpendicular height, h, is increasing at the rate of 0.2 cm/s. Find the rate at which the volume, V, is changing when >= 2 cm and h=3 cm. QUESTION 5: (a) Establish a reduction formula for [sin" xcx in the form (15) 1 n-1 I =--sin' xcosx+ -2 I; and hence determine [sin³ xcx. (15) Find the length of the curve x=2 cose, y = 2 sin between the points e=0 and e= QUESTION 6: (10) (a) The parametric equations of a curve are x = 32, y = 3t. Find the volume generated when the plane figure bounded by the curve, the x-axis and the ordinates corresponding to f=0 and t = 2, rotates about the x-axis. (15) (b) Using Simpson's rule with 6 intervals, evaluate: √ √(cosxcx, correct to three decimal places. Page 3 of 3 381 words English (United States) Text Predictions: On Accessibility: Unavailable (10) Comments CK Editing Share Focus + 80%

W AutoSave Off H 2 MAT 291 (SUPPL EXAM,JAN 2011) - Compatibility Mode Saved File Home Insert Draw Design Layout References (b) Search CK Mailings Review View Help Find the radius of curvature and the centre of curvature of the curve: Comments Editing at the point (12) (15) QUESTION 3: (a) The motion of a particle performing damped vibrations is given by y = e¹ sin 2t, (b) (c) Page 2 of 3 381 words English (United States) Text Predictions: On y being the displacement from its mean position at time t. Show that y is a 1 maximum when t=- tan (2) and determine this maximum displacement to three significant figures. Find the range of values of x for which the following series is convergent: (x-2), (x-2)(x-2)³ (x-2)" +...+ +... 1 2 3 n By the use of Maclaurin's series, obtain the expansion of sin including the term x³. Accessibility: Unavailable (10) (10) -1 x, up to and (5) 2 Share Focus + 100% W AutoSave Off ひ MAT 291 (SUPPL EXAM,JAN 2011) - Compatibility Mode Saved . Search File Home Insert Draw Design Layout References Mailings Review View Help QUESTION 4: (a) Suppose V a²v a²v a²v Simplify (10) (b) The base radius of a cone, 7, is decreasing at the rate of 0.1 cm/s while the perpendicular height, h, is increasing at the rate of 0.2 cm/s. Find the rate at which the volume, V, is changing when >= 2 cm and h=3 cm. QUESTION 5: (a) Establish a reduction formula for [sin" xcx in the form (15) 1 n-1 I =--sin' xcosx+ -2 I; and hence determine [sin³ xcx. (15) Find the length of the curve x=2 cose, y = 2 sin between the points e=0 and e= QUESTION 6: (10) (a) The parametric equations of a curve are x = 32, y = 3t. Find the volume generated when the plane figure bounded by the curve, the x-axis and the ordinates corresponding to f=0 and t = 2, rotates about the x-axis. (15) (b) Using Simpson's rule with 6 intervals, evaluate: √ √(cosxcx, correct to three decimal places. Page 3 of 3 381 words English (United States) Text Predictions: On Accessibility: Unavailable (10) Comments CK Editing Share Focus + 80%

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 98E

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