If the functionf(x) satisfies x→1limx2−1f(x)−2=π evaluate x→1limf(x)

x→1limx2−1f(x)−2=π⇒limx→1(x2−1)limx→1(f(x)−2)=π⇒x→1lim(f(x)−2)=πx→1lim(x2−1)⇒x→1lim(f(x)−2)=π(12−1)⇒x→1lim(f(x)−2)=0⇒x→1limf(x)−x→1lim2=0⇒x→1limf(x)−2=0∴ x→1limf(x)=2

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If the functionf(x) satisfies _{x 1}{f ( x )-2}{x^{2}-1}= ev

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If the function $f (x)$ satisfies $x \to 1 lim \frac{f ( x ) - 2}{x ^{2} - 1} = π$ evaluate $x \to 1 lim f (x)$

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Eleanor Discussed

If the function

f (x)

satisfies

x \to 1 lim \frac{f ( x ) - 2}{x ^{2} - 1} = π

evaluate

x \to 1 lim f (x)

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

x \to 1 lim \frac{f ( x ) - 2}{x ^{2} - 1} = π

\Rightarrow \frac{lim _{x \to 1} ( f ( x ) - 2 )}{lim _{x \to 1} ( x ^{2} - 1 )} = π

\Rightarrow x \to 1 lim (f (x) - 2) = π x \to 1 lim (x^{2} - 1)

\Rightarrow x \to 1 lim (f (x) - 2) = π (1^{2} - 1)

\Rightarrow x \to 1 lim (f (x) - 2) = 0

\Rightarrow x \to 1 lim f (x) - x \to 1 lim 2 = 0

\Rightarrow x \to 1 lim f (x) - 2 = 0

∴ x \to 1 lim f (x) = 2

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Question Text	If the function $f (x)$ satisfies $x \to 1 lim \frac{f ( x ) - 2}{x ^{2} - 1} = π$ evaluate $x \to 1 lim f (x)$
Answer Type	Text solution:1
Upvotes	150

If the functionf(x) satisfies x→1lim​x2−1f(x)−2​=π evaluate x→1lim​f(x)

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If the function $f (x)$ satisfies $x \to 1 lim \frac{f ( x ) - 2}{x ^{2} - 1} = π$ evaluate $x \to 1 lim f (x)$