sum approximations

Find a Riemann - sum approximation of the area of the plane under the curve y = x 2 on [0, 2] using left end points and regular portion of order 4. => 1.75 sq.units or 2.25 sq.units or 7 sq.units or 0.5 sq.units or 3.5 sq.units..

Approximate the area of the plane region under the curve y = ln x over [2, 5] by Riemann sum with a regular partition of order 6 and using midpoints. => 3.631 sq.units or 2.883 sq.units or 2.168 sq.units or 4.041 sq.units or 4.441 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 under the curve y = 1 x over [2, 5] by Riemann sum with a regular partition of order 3 and using mid points. => 0.685 sq.units or 1.609 sq.units or 0.507 sq.units or 0.907 sq.units or 0.622 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..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, intervals Newton's method (..

The definition, , can be explained in another way also. We rewrite above definition as Here the first term is hf (a). It is the area of the rectangle marked as 1 in figure below (because h and f (a) are the adjacent sides of this rectangle). Similarly, the second term hf (a+h) is the area of the re..

Introduction - We use specific number of digits to denote an exact value of a number for required accuracy. The digits used for such a purpose are called significant figures. Suppose a measurement is recorded as 0.6204 cm. It means that the measurement was made correct to the nearest 0.0001 cm. The..

where l is a finite number and is equal to np. The sum of the probabilities P(X = r) or simply P(r) for r = 0, 1, 2, is 1. This can be seen by putting r = 0, 1, 2, in (4) and adding all the probabilities. Also, each of the probabilities is a non-negative fraction. This leads to the distri..

of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficients in the expressio..