104Math. Find the equation of the parabola and sketch it in the exercises 10-18:

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1 KING SAUD UNIVERSITY COLEGE OF SCIENCE DEPARTMENT OF MATHEMATICS Math Prof Messaoud Bounkhel List of Eercises: Chapter [Parabola] Find the elements of the parabola and sketch it in the eercises -9: ( ) ( ) ( ) 9 Find the equation of the parabola and sketch it in the eercises -: The verte V is the origin and the focus F is (,) The verte V is the origin and the equation of the directri is =- The verte V is the origin and the equation of the directri is = The verte V is (,) and the focus F is (,) The verte V is (-,) and the equation of the directri is = The focus F is (,) and the equation of the directri is =- The focus F is (,) and the equation of the directri is = The verte V is (,-) and the equation of the directri is =- The verte V is (,-) and the focus F is (,)

2 [Ellipse] Find the elements of the ellipse and sketch it in the eercises 9-: Find the equation of the ellipse and sketch it in the eercises -: The foci are F (,) and F (,), and it passes through the point A (,) The vertices are V (,) and V (,), and the length of the minor ais is The foci are F (,) and F (,), and it passes through the point A (,) The vertices are V (,) and V (,), and the length of the minor ais is [Hperbola] Find the elements of the hperbola and sketch it in the eercises -: Find the equation of the hperbola and sketch it in the eercises -: The foci are F (,) and F (,), and has one verte on (,) The vertices are V (,) and V (,), and has one focus on (,) The foci are F (,) and F (,), and the distance beteen the vertices is The vertices are V (,) and V (, ), and the foci are F (,) and F (, )

3 [Miscellaneous] Find the elements of the conic section: and sketch it Find the equation of the parabola ith focus F (, ) and its directri ith equation: Find the elements of the conic section: 9 and sketch it Find the equation of the ellipse ith foci F (,) and F (,) and ith vertices V (,) and V (,) 9 Find the equation of the ellipse ith foci F (,) and F (,) and the length of its major ais is Find the elements of the conic section: 9 and sketch it Find the elements of the conic section: and sketch it Find the equation of the hperbola ith foci F (,) and F (, ) and the distance beteen the vertices is Find the equation of the hperbola ith vertices V (,) and V (,) and, ith foci F (,) and F (,) Find the equation of the hperbola ith vertices V (,) and V (,) and the equations of the asmptotes are and Find the equation of the hperbola ith vertices V (, ) and V (,) the distance beteen the foci is and

4 Chapter [Matrices and determinants] Compute (if possible): BA and AB for the folloing matrices: ) A B ) A B ) A B ) A B Evaluate the folloing multiplications: ) 9 ) ) 9 ) 9 )

5 ) ) ) 9) ) ) ) Evaluate the folloing determinants: ) 9 ) )

6 ) ) ) ) Chapter [Linear Sstems] Solve b one of the folloing methods (Cramer's Rule, Gauss elimination, and Gauss- Jordan Elimination) the folloing linear sstems: ) ) ) 9 )

7 ) 9 9 ) ) 9 ) 9) 9 ) u u b c b a c b b a )

8 Chapter [Integrals] Compute the folloing integrals: ) ( ) sin( ) d + d d + ) ( ) ln d sin d d ( ) sin d d ) 9 cos d d ( ) ln d ln( ) d d ) ( )( ) cos( ) d + d - sin ) d ( + ) ( + ) ( ) sin d d cos ) ( ) sin( ) d + d d + ) ( ) ln d d ( )( ) d Chapter [Applications of Integrals] Find the area of the regions determined b the curves: ) =, =, = ) =, =, = ) ),,,,, ),, ),,

9 ) =, = -, = ),,, 9) =, =, = ),,, ), ),,, cos ),,, ), ), ),,, ), ),,, 9), ), Find the volume of the solid of revolution generated b rotation about one of the coordinate aises of the region R limited b the folloing curves: =,, = (rotated about the -ais) =, =, =, and = + (rotated about the -ais) =, =-- and = (rotated about the -ais)

10 =, =, and = + (rotated about the -ais),, (rotated about the -ais),,, (rotated about the -ais), (rotated about the -ais), (rotated about the -ais) 9, (rotated about the -ais), (rotated about the -ais),, (rotated about the -ais),, (rotated about the -ais),, (rotated about the -ais),, (rotated about the -ais), 9,, (rotated about the -ais),, (rotated about the -ais), (rotated about the -ais)

11 Chapter Partial Differentiation In eercises - find all first and second partial derivatives of the given functions: f (, ) f (, ) e at (,) cos( ) f ( p, q) q p at (-,) cos(/ ) f (,, ) 9 ln( ) at (,,) e In the folloing eercises use the chain rule to find t, t d dt t cos sin, t at t ln( ) t, t / e t /, t tan t, t at t

12 In the folloing eercises use the chain rule to find t and s sin s t, st, sln t, s t at (, ) ln s t, st at (,) 9 cos s t, s s t, s t, s t at (,) d In the folloing eercises find d / / In the folloing eercises find sin and 9 e e e cos

13 Chapter Introductor Differential Equations In the folloing eercises solve the given differential equations: d d ( ) ' ()= ' ( ) d sec tan () d cos e sin 'cos ' ' e ' ()= 9 ' cos( e ) d d d d ()= ' sin ( / ) d d sec tan ( / ) ' d d > e d ()= d

Math 180 Chapter 10 Lecture Notes. Professor Miguel Ornelas

Math 180 Chapter 10 Lecture Notes Professor Miguel Ornelas 1 M. Ornelas Math 180 Lecture Notes Section 10.1 Section 10.1 Parabolas Definition of a Parabola A parabola is the set of all points in a plane