Problem #3: Sketch the polar curve r = cos(₂).(A)(D)(G)LOProblem #3: Select vSave(B)(E)(H)DE@(C)(F)

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Answered: Problem #3: Sketch the polar curve r =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. (i) Find the polar coordinate of the point P(x, y) = (1, v3).Plot the graph (ii) Find the cartesian coordinate of the point P(r, 0) = (-2,). Plot the graph
3. Which of the following is the equation of the tangent at the point 0 3 line to the polar curve r= se. V3 (a) 5. 3V3 (b) (c) V3 T+1 (d)
ii. Find parametric equations for the Line through (7, 5) and (-5, 7) 7. Calculate dy/dx at the point indicated: f(0) = (7tan 0, cos O), 0=a/4
abcoso. (b) The length in first quadrant of the curve x²/3 + y²/3 = a²/3 is given by 6ac/2 where %3D parametric equations of curve are x = a cos 8,y = a sin 0. Compute the value of c. Also find the length in first quadrant of the curve (x/a)?/3 + (y/b)*/3 =1 where parametric equations of curve are x = a cos 0, y = b sin*e.
37. The Cartesian equation of the polar curve 2 = 2a' sin 20 is A. 1? + y? = 4a²xy B. (z* + 3° )° = a°zy C. a? + y? = 4xy D. (z? + y² )° = 4a²zy
6 (1). Consider the curve C of equation (x²-2y+y?)? = x²+y². Among the options listed, select the one that correctly shows a possible equation for C in polar coordinates and the equation of a line tangent to the pole. A) C:r=1+2 sin(0), With tangent to the pole 27 0 = 3 B) C :r=1+2 sin(0), With tangent to the pole 77 0 = 6. C) C:r=1- 2 cos(8), With tangent to the pole 0 = D) C:r=1+ 2 cos(0), 27 0 = 3 %3D With tangent to the pole
5. Consider the polar curve r(0) -2 cos 0 (a) Circle the polar curve that matches the r(0) above. Give supporting reasons why you chose that particular curve. (a) (c) у VT X X (b) (d) y X X
COs 6), = T/4 8. i. Convert (x, y)= (-v3, 1) to polar coordinate. ii. Convert r=7 sin O to Cartesian equation in terms of x and y.
5. Find the maximum height above the x-axis of the polar curve r = 2+2 cos(0).
A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:
2. The substitution u=cosx is suitable to solve the following integral: sin'x cos!5x O False O True
Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t),y = 2 cos(t); 0 st < 2n (a) y² – x² = 2 (b) x² + y² = 2 () x² + y² = 4 (d) y = x² – 4 (e) y = x² - 2

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Problem #3: Sketch the polar curve r = cos(₂). (A) (D) (G) X O C Problem #3: Select C (B) (E) (H) *08 (C) (F) * &

Problem #3: Sketch the polar curve r = cos(₂). (A) (D) (G) X O C Problem #3: Select C (B) (E) (H) 08 (C) (F) &