Recent Military, Naval, and Civil Service Examination Papers in Mathematics, with Answers and Hints for SolutionWilliam Tomlin, 1874 - 116 σελίδες |
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Σελίδα 21
... coefficients of a3 , and of x " , in the expansions of ( 1 - x ) -2 , and ( 1 - x ) . - - If n ( n − 1 ) ( n − 2 ) ... ( n − r + 1 ) = N Cr prove that n + 1 1199 1.2.3 ... r C1 = C + Cr 22 g 5. Express 209 , and √ ( 10 ) in the form ...
... coefficients of a3 , and of x " , in the expansions of ( 1 - x ) -2 , and ( 1 - x ) . - - If n ( n − 1 ) ( n − 2 ) ... ( n − r + 1 ) = N Cr prove that n + 1 1199 1.2.3 ... r C1 = C + Cr 22 g 5. Express 209 , and √ ( 10 ) in the form ...
Σελίδα 26
... coefficients of x " ( n unrestricted ) and of sinx . Differentiate ( 1 ) ( + 2 2 ( 2 ) ( logx ) * , ( 3 ) cos ( tan ̄x ) . X 5. Find the 7th differential coefficient of x " e " and prove that if mx " 72 y " -ny + ( n - 1 ) x = a , then ...
... coefficients of x " ( n unrestricted ) and of sinx . Differentiate ( 1 ) ( + 2 2 ( 2 ) ( logx ) * , ( 3 ) cos ( tan ̄x ) . X 5. Find the 7th differential coefficient of x " e " and prove that if mx " 72 y " -ny + ( n - 1 ) x = a , then ...
Σελίδα 34
... coefficient if r be greater than n + 1 9 2 and when ( n ) is integral and negative , show that the coefficients continually increase . Find by the binomial theorem an approximate value to ( 1013 ) . PURE MATHEMATICS . 1. Express ( 11 ) ...
... coefficient if r be greater than n + 1 9 2 and when ( n ) is integral and negative , show that the coefficients continually increase . Find by the binomial theorem an approximate value to ( 1013 ) . PURE MATHEMATICS . 1. Express ( 11 ) ...
Σελίδα 35
... coefficient of an equation , prove that p + 1 is a superior limit of the roots . 9. State how the derived function f ' ( x ) may be employed to ascertain the existence of equal roots in the equation f ( x ) = 0 . Ex . x3 - 5x - 8x + 48 ...
... coefficient of an equation , prove that p + 1 is a superior limit of the roots . 9. State how the derived function f ' ( x ) may be employed to ascertain the existence of equal roots in the equation f ( x ) = 0 . Ex . x3 - 5x - 8x + 48 ...
Σελίδα 40
... coefficients , and express the general form of the coefficient of x " . Assuming that log , ( 1 + x ) can be so expanded , find the series . Expand to three terms 7. If u = P -x n 11 + e 2 where P and Q are functions of x which ...
... coefficients , and express the general form of the coefficient of x " . Assuming that log , ( 1 + x ) can be so expanded , find the series . Expand to three terms 7. If u = P -x n 11 + e 2 where P and Q are functions of x which ...
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ... Braithwaite Arnett Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
acres Algebra angular points ARITHMETIC AND LOGARITHMS arithmetic series axis base bisects the angle cent centre of gravity chords coefficient continued fraction cosine cubic cuts the circle Define Describe a circle diameter distance Divide ellipse equilateral Euclid expression exterior angle feet Find by Practice Find the equation find the number Find the value forces acting Geometry given circle given straight line given triangle inches inscribed intersection latus rectum least common multiple logarithms METCALFE AND SON Mixed Mathematics Multiply parabola parallel parallelogram particle perpendicular places of decimals pressure produced prove PURE MATHEMATICS ratio rect rectangle contained right angles shew sides simple interest spherical triangle string subtended Subtract surface tangent things taken Todhunter's triangle ABC TRIGONOMETRY velocity vertex vertical vis viva weight yards
Δημοφιλή αποσπάσματα
Σελίδα 83 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 72 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 72 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 17 - Parallelograms on the same base, and between the same parallels, are equal to one another.
Σελίδα 54 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 12 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 82 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 44 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.
Σελίδα 82 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 1 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.