Limx- a-fx-l- limx- a-gx-0- limx- a-hx-m -then limx- a-fx-gx-hx-

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Byju's Answer

Standard XII

Mathematics

Eccentricity of Ellipse

limx→ a-fx=l,...

Question

$lim x \to a^{-} f (x) = l$ ,
$lim x \to a^{-} g (x) = 0$ ,
$lim x \to a^{-} h (x) = m$ ,then
$lim x \to a^{-} (f (x) - g (x) + h (x)) =$

does not exist

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l

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l + m

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cannot be determined

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Solution

The correct option is C $l + m$
Since, the limit of a function can be split into it's respective components,
$l i m_{x \to a^{-}} [f (x) - g (x) + h (x)]$
$= (l i m_{x \to a^{-}} f (x)) - (l i m_{x \to a^{-}} g (x)) + (l i m_{x \to a^{-}} h (x))$
$= l - 0 + m$
$= l + m$

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limx→a−f(x)=l,limx→a−g(x)=0,limx→a−h(x)=m ,thenlimx→a−(f(x)−g(x)+h(x))=

The correct option is C l+mSince, the limit of a function can be split into it's respective components,limx→a−[f(x)−g(x)+h(x)]=(limx→a−f(x))−(limx→a−g(x))+(limx→a−h(x))=l−0+m=l+m

$lim x \to a^{-} f (x) = l$ ,
$lim x \to a^{-} g (x) = 0$ ,
$lim x \to a^{-} h (x) = m$ ,then
$lim x \to a^{-} (f (x) - g (x) + h (x)) =$

The correct option is C $l + m$
Since, the limit of a function can be split into it's respective components,
$l i m_{x \to a^{-}} [f (x) - g (x) + h (x)]$
$= (l i m_{x \to a^{-}} f (x)) - (l i m_{x \to a^{-}} g (x)) + (l i m_{x \to a^{-}} h (x))$
$= l - 0 + m$
$= l + m$