f ( x ) = { 4 x − 3 , x < 1 x 2 x ≥ 1 , then lim x → 1 f ( x ) = Options: A . &nbsp 1 B . &nbsp − 1 C . &nbsp 0 D . &nbsp 0

Answer: Option A : A lim x → 1 − f ( x ) = lim x → 1 − ( 4 x − 3 ) = 1 lim x → 1 + f ( x ) = lim x → 1 + x 2 = 1 Since LHL = RHL ⇒ lim x → 1 f ( x ) = 1

f(x)={4x−3,x<1x2x≥1, then limx→1f(x)=

Discussion Forum : Limits Continuity And Differentiability

Question -

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

Options:

A .

1

B .

- 1

C .

0

D .

0

Answer: Option A
:
A

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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Discussion Forum : Limits Continuity And Differentiability

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