f x - left matrix 4 x-3- - x-1 1x- 2 - x lgeq 1lendmatrix right- thenlimfx - 1 fx-A- 1B- -1C- 0D- 0

The correct option is A 1x→ 1^ lim f(x) = x→ 1^ lim (4x 3) = 1 x→ 1^+lim f(x) = x→ 1^+limx^2 = 1 Since LHL = RHL ⇒x→ 1lim f(x) = 1 ...

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Standard XI

Mathematics

Existence of Limit

f x = left m...

Question

$f (x) = {\begin{matrix} 4 x - 3, & x < 1 x^{2} & x \geq 1 \end{matrix},$ then
$lim x \to 1 f (x) =$

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Solution

The correct option is A $1$
$lim x \to 1^{-} f (x) = lim x \to 1^{-} (4 x - 3) = 1$
$lim x \to 1^{+} f (x) = lim x \to 1^{+} x^{2} = 1$
Since LHL = RHL
$\Rightarrow lim x \to 1 f (x) = 1$

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f(x)={4x−3,x<1x2x≥1, then limx→1f(x)=

The correct option is A 1limx→1−f(x)=limx→1−(4x−3)=1 limx→1+f(x)=limx→1+x2=1 Since LHL = RHL ⇒limx→1f(x)=1

$f (x) = {\begin{matrix} 4 x - 3, & x < 1 x^{2} & x \geq 1 \end{matrix},$ then
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The correct option is A $1$
$lim x \to 1^{-} f (x) = lim x \to 1^{-} (4 x - 3) = 1$
$lim x \to 1^{+} f (x) = lim x \to 1^{+} x^{2} = 1$
Since LHL = RHL
$\Rightarrow lim x \to 1 f (x) = 1$