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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
Frederick bought six books which cost d dollars each. What is the total cost of the books? Frederick would multiply the number of books, 6, through how much each one costs, d.
Example of Word problem: There is a man who is 21 years older than his son. 5 years ago he was four times as old as his son. How older are both now? Solution: Step 1
Assume that the amount of air in a balloon after t hours is specified by V (t ) = t 3 - 6t 2 + 35 Calculate the instantaneous
find h in the parallelogram
The logarithm of a provided number b to the base 'a' is the exponent showing the power to which the base 'a' have to be raised to get the number b. This number is defined as log a
Example of Least Common Denominator: Example: Add 1/7 +2 /3 + 11/12 + 4/6 Solution: Step 1: Find out primes of each denominator. 7 = 7 (already is
Equations of Lines In this part we need to take a view at the equation of a line in R 3 . As we saw in the earlier section the equation y = mx+b does not explain a line in R
3/4=x/23.
what is the formula fore life
Trapezoid Rule - Approximating Definite Integrals For this rule we will do similar set up as for the Midpoint Rule. We will break up the interval [a, b] into n subintervals of
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