2 x-3 - x leq 0 13x-1 - x-0lendmatrix right-

Here f(x) = { 2x+3 amp; x ≤ 0 3 (x+1) amp; x gt; 0 . Now x → 0lim f(x) = x → 0lim 2x+3 = 2 × 0 + 3 = 3 x → 0limf(x)= x → 0lim 3(x+1) = 3 (1+1) = 3 ...

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Byju's Answer

Standard XII

Mathematics

Indeterminate Forms

2 x+3 & x leq...

Question

Find $lim x \to 0$ f(x) and $lim x \to 1$ f(x) where f(x)= ${\begin{matrix} 2 x + 3 & x \leq 0 3 (x + 1) & x > 0 \end{matrix}$

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Solution

Here f(x) = ${\begin{matrix} 2 x + 3 & x \leq 0 3 (x + 1) & x > 0 \end{matrix}$

Now $lim x \to 0$ f(x) = $lim x \to 0 2 x + 3 = 2 \times 0 + 3$ = 3

$lim x \to 0 f (x) = lim x \to 0$ 3(x+1) = 3 (1+1)

= 3 $\times$ 2 = 6.

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Find limx→0 f(x) and limx→1 f(x) where f(x)= {2x+3x≤03(x+1)x>0

Here f(x) = {2x+3x≤03(x+1)x>0 Now limx→0 f(x) = limx→0 2x+3=2×0+3 = 3 limx→0f(x)=limx→0 3(x+1) = 3 (1+1) = 3 × 2 = 6.

Find $lim x \to 0$ f(x) and $lim x \to 1$ f(x) where f(x)= ${\begin{matrix} 2 x + 3 & x \leq 0 3 (x + 1) & x > 0 \end{matrix}$

Here f(x) = ${\begin{matrix} 2 x + 3 & x \leq 0 3 (x + 1) & x > 0 \end{matrix}$

Now $lim x \to 0$ f(x) = $lim x \to 0 2 x + 3 = 2 \times 0 + 3$ = 3

$lim x \to 0 f (x) = lim x \to 0$ 3(x+1) = 3 (1+1)

= 3 $\times$ 2 = 6.