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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
give an example of a relation R that is transitive while inverse of R is not
In a survey of 85 people this is found that 31 want to drink milk 43 like coffee and 39 wish tea. As well 13 want both milk and tea, 15 like milk & coffee, 20 like tea and coffee
You plan to retire when you are 65th years old. You are now 25 years old. You plan to buy a pension annuity that will pay you $100,000 per year starting one year after you turn 6
find the simple interest on Rs. 68,000 at 50/3 per annum for 9 month
What is Exponents values? Exponents were invented as a quick way to show that you are multiplying a number by itself several times. It's too much trouble to write something
Example of Linear Equations: Solve the equation 2x + 9 = 3(x + 4). Solution: Step 1. Using Axiom 2, subtract 3x and 9 from both sides of the equation. 2x + 9 = 3(
Steps in solving graphical method of simultaneous linear equations
Example of Rounding Off: Example: Round off the subsequent number to two decimal places. 6.238 Solution: Step 1: 8 is the number to the right of t
What is Multiplying Fractions ? The rule for multiplying fractions is to "multiply across": Multiply the numerators to get the numerator of the answer. Multiply the den
Integration Techniques In this section we are going to be looking at several integration techniques and methods. There are a fair number of integration techniques and some wil
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