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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Definition of inverse functions : Given two one-to-one functions f ( x ) and g ( x ) if ( f o g ) ( x ) = x AND ( g o f ) ( x ) = x then we say that f ( x ) & g ( x ) are i
Integral Test- Harmonic Series In harmonic series discussion we said that the harmonic series was a divergent series. It is now time to demonstrate that statement. This pr
1. A train on the Bay Area Rapid Transit system has the ability to accelerate to 80 miles/hour in half a minute. A. Express the acceleration in miles per hour per minute. B
Recognizes the absolute extrema & relative extrema for the following function. f ( x ) = x 2 on [-1, 2] Solution: As this function is simpl
Two circles touch each other externally: Given: Two circles with respective centres C1 and C2 touch each other externaly at the point P. T is any point on the common tangent
What is a Function, Anyway? Domain? Range? Next time you're at a fast-food restaurant, take a look at the price list. It may look something like this: • Hamburger.............
Definition of Natural exponential function: The natural exponential function is f( x ) = e x where, e= 2.71828182845905........ . Hence, since e > 1 we also know that e x
how to do mathematical proofs
Q. What is a Mixed Number? Ans. A mixed number is an integer, along with a fractional part, which has the same sign. (Therefore, a mixed number always has two parts.) M
We are here going to begin looking at nonlinear first order differential equations. The first type of nonlinear first order differential equations which we will see is separable di
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