first order approximations

We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Numbers can be rounded off to any given place. When we round off a number to any given place we get an approximate value of the numbe..

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) + The successi..

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 sa..

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 ..

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..

When the pressure in the discharge tube is less than 10 - 4 mm of Hg, the discharge tube starts showing fluorescence. When this fluorescence was investigated, it was found that the fluorescence consisted of beams of negatively charged electrons. These electrons emanate normally from the cathode. As..

Dobereiner's Triads - 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 masses. In the year 1829, Johann Wolfgang Dobereiner, a German scientist, was t..