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By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9. Answer: Let make four groups of two numbers from 1 to 8 like
The sum of the smallest and largest multiples of 8 up to 60 is?
Fundamental Theorem of Calculus, Part II Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =
Q. Definition of Logarithms? Ans. A logarithm to the base a of a number x is the power to which a is raised to get x. In equation format: If x = a y , then log a x
Horizontal tangents for Parametric Equations Horizontal tangents will take place where the derivative is zero and meaning of this is that we'll get horizontal tangent at value
what is fraction?
Mathematical Problem Solving In 1945, mathematician George Polya (1887-1985) published a book titled How To Solve It in which he demonstrated his approach to solving problems.
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale
#What is an easy way to find the area of any figure
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