second order approximations

Approximation - We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2..

We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (3 x 1) + Th..

An economist wishes to estimate the average monthly rent of houses in a large city to within $25 with 99% confidence. A study of 70 houses in the city found that 49 houses had their rent as $1,000. How many houses must be surveyed in order to be justified in assuming that the sample propo..

Approximate the area of the plane region under the curve y = x 4 over [- 1, 1] by Riemann sum with a regular partition of order 4 using mid points. => 0.316 sq.units or 0.6359 sq.units or 0.6320 sq.units or 0.3199 sq.units or 0.0039 sq.units..

Approximate the area of the plane region under the curve y = e x over [- 2, 2] by Riemann sum with a regular partition of order 4 and using right end points. => 10.474 sq.units or 8.756 sq.units or 4.0853 sq.units or 9.123 sq.units or 11.474 sq.units..

Approximate the area of the plane region under the curve y = 3 x over [1, 3] by Riemann sum with a regular partition of order 4 using left end points. => 9 sq.units or 10.5 sq.units or 11 sq.units or 7.5 sq.units or 9.5 sq.units..

Approximate the area of the plane region under the curve y = 2 x - 1 over [3, 7] by Riemann sum with a regular partition of order 4 and using left end points. => 2.567 sq.units or 1.90 sq.units or 2.167 sq.units or 1.167 sq.units or 1.791 sq.units o..

During selection trials for the Olympic games, the qualifying time set for 100 metres sprint is 11 seconds. Lily′s current speed for 100 metres sprint is 13 seconds. How much time should Lily save in order to qualify? => 4 seconds or 3 seconds..

.e., its reaction is fast and more exothermic. This also implies that the reverse reaction becomes more difficult i.e., the more reactive a metal, the more difficult it is to extract from its ore. The metal is also more susceptible to corrosion with oxygen and water. The reactivity series can be es..

In the famous atomic theory of John Dalton (1805), it was suggested that the atoms of an element have a characteristic mass. So, attempts were made to classify elements on the basis of their atomic masse..