Composition of Functions

Composition of Functions

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The term "composition of functions" (or "composite function") refers to the combining of functions in a manner where the output from one function becomes the input for the next function.

In math terms, the range (the y-value answers) of one function becomes the domain (the x-values) of the next function.

COMPOSITION OF FUNCTIONS

 

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COMPOSITION OF FUNCTIONS

 

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De Moivre's Theorem

De Moivre's Theorem

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(1) If n is any rational number, then (cos θ + i sin θ)n = cos nθ + i sin nθ.

(2) If z = (cos θ1 + i sin θ1) (cos θ2 + i sin θ2) (cos θ3 + i sin θ3)………… (cos θn + i sin θn)

then z = cos (θ1 + θ2 + θ3 + ……… + θn) + i sin (θ1 + θ2 + θ3 + ……… + θn)

where θ1 + θ2 + θ3 + ……… + θn ∈ R.

DE MOIVRE'S THEOREM

 

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Neutralization Reaction

Neutralization Reaction

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The reaction of an acid and a base is called a neutralisation reaction. In this reaction, the acidity of an acid is neutralised by an alkali. At the same time, the alkalinity of the alkali is neutralised by the acid. A salt and water are the only products of a neutralisation reaction.

Acid + alkali → salt + water

NEUTRALIZATION REACTION

 

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NEUTRALIZATION REACTION

 

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Integration Rules

Integration Rules

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Integration Rules

Chain rule :

∫u.v dx = uv1 – u'v2 + u''v3 – u'''v4 + ……… + (–1)n­–1 un–1vn + (–1)n ∫un.vn dx

Where  stands for nth differential coefficient of u and stands for nth integral of v.

Sum Rule

∫(f + g) dx = ∫f dx + ∫g dx

Difference Rule

∫(f - g) dx = ∫f dx - ∫g dx

INTEGRATION RULES

 

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HETEROTROPH DEFINITION

 

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Heterotroph Definition

Heterotroph Definition

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Heterotrophic Nutrition:

It is a mode of nutrition in which the organisms obtain readymade organic food from outside sources. The organisms that depend upon outside sources for obtaining organic nutritens are called heterotrophs. Heterotrophic nutrition is of three types - saprophytic, parasitic and holozoic.

HETEROTROPH DEFINITION

 

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Latent Heat

Latent Heat

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Latent Heat

Specific Latent Heat

The amount of heat required to change the phase of a substance depends on the mass and the type of material of the substance.

A small ice cube melts quickly but a large block of ice melts very slowly.

100 J of heat energy can melt a large amount of wax, but the same amount of heat can only melt a small amount of iron.

The specific latent heat of a substance is the amount of heat required to change the phase of 1 kg of the substance at a constant temperature.

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Binomial Nomenclature

Binomial Nomenclature

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It was Proposed by Carolus Linnaeus.

• According to this system of nomenclature, each animal or plant is given two names : the first one is the generic name and the second one is the name of the species.
• Scientific names are always in Latin.
• The first letter of the generic name is always capitalized and that of the specific name is written in small letter. For example, the scientific name of frog is Rana tigrina, in which Rana is the generic name and tigrina is the name of the species.

BINOMIAL NOMENCLATURE

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BINOMIAL NOMENCLATURE

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