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META-HUB Latest Questions

Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: February 24, 2023In: Calculus ( කලනය )

Tangent line to a curve

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How can you compare the following ways of defining a tangent line to a curve at a point P(α,β) with examples? 1)A straight line meet the curve at the point P with the curve appearing in only one side of the ...

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Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: February 24, 2023In: Calculus ( කලනය )

Existence of a local minimum

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Second derivative being a positive value at a point is not a necessary and sufficient condition to exist a local minimum at that particular point and the proof of this was already asked in an advanced level exam. If so ...

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Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: February 24, 2023In: Geometry ( ජ්‍යාමිතිය )

Equation of the tangent line

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In general can you use the standard form y – β = m(x –  α)  of a straight line of gradient m , going through a point (α,β) in the case of finding equation of a tangent line drawn to ...

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Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: February 24, 2023In: Mechanics ( යාන්ත්‍ර විද්‍යාව )

Centre of mass in advanced level statics

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Is this question correct or else what should be the correct way of asking the following question? Find the position of centre of gravity of a cone of height h and base radius r

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Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: February 24, 2023In: Arithmetic ( අංක ගණිතය )

Irrationality of the constant e of exponential function.

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As you know we teach our students, sum of rational numbers is also a rational number as a property of rational numbers when we introduce real numbers in the beginning of advanced level mathematics. But though the constant e is ...

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Janaka Rodrigo
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Janaka RodrigoLevel 2
Asked: February 23, 2023In: Algebra ( වීජ ගණිතය )

Composite functions

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1)What are the conditions required to be satisfied to exist the composite function f(g(x))? 2)Do we need range of g to be a subset of domain of f or is intersection of mentioned range and domain sufficient and what is the ...

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