If fx-2x-b if x-ax-d if x- a and limx- afx-l- then l is equal to

Lim_x→ af(x)=l nbsp; ⇒lim_x→ a^ (2x+b)=lim_x→ a^+(x+d)=l ∴ l=2a+b⋯(1) and nbsp; l=a+d⋯(2) By eleminating a from (1) and (2), we get l=2d b ...

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Standard XII

Mathematics

Evaluation of Limit

If fx=2x+b ...

Question

If $f (x) = {\begin{matrix} 2 x + b if x < a x + d if x \geq a \end{matrix}$ and $lim x \to a f (x) = l,$ then $l$ is equal to

b + d

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b - d

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2 d + b

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2 d - b

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Solution

The correct option is D $2 d - b$
$lim x \to a f (x) = l$
$\Rightarrow lim x \to a^{-} (2 x + b) = lim x \to a^{+} (x + d) = l$
$∴ l = 2 a + b \dots (1)$ and
$l = a + d \dots (2)$
By eleminating $a$ from $(1)$ and $(2),$ we get
$l = 2 d - b$

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{sin (a x^{2} + b x + c)}{x^{2} - 1}, & if x < 1 - 1, & if x = 1 a sgn (x + 1) cos (2 x - 2) + b x^{2}, & if 1 < x \leq 2 \end{matrix}

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Evaluation of Limit

Standard XII Mathematics

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If f(x)={2x+b if x<ax+d if x≥a and limx→af(x)=l, then l is equal to

The correct option is D 2d−blimx→af(x)=l ⇒limx→a−(2x+b)=limx→a+(x+d)=l ∴l=2a+b⋯(1) and l=a+d⋯(2) By eleminating a from (1) and (2), we get l=2d−b

If $f (x) = {\begin{matrix} 2 x + b if x < a x + d if x \geq a \end{matrix}$ and $lim x \to a f (x) = l,$ then $l$ is equal to

The correct option is D $2 d - b$
$lim x \to a f (x) = l$
$\Rightarrow lim x \to a^{-} (2 x + b) = lim x \to a^{+} (x + d) = l$
$∴ l = 2 a + b \dots (1)$ and
$l = a + d \dots (2)$
By eleminating $a$ from $(1)$ and $(2),$ we get
$l = 2 d - b$