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If f(x)=(x^(2)-3x+2)/(x^(2)-7x+12), then...

If `f(x)=(x^(2)-3x+2)/(x^(2)-7x+12),` then which of the following limits exists?
`(i)lim_(xtooo) sin^(-1)f(x)" "(ii)lim_(xtooo) cos^(-1)f(x)`

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the function \( f(x) = \frac{x^2 - 3x + 2}{x^2 - 7x + 12} \) and determine the limits as \( x \) approaches infinity for both \( \sin^{-1}(f(x)) \) and \( \cos^{-1}(f(x)) \). ### Step-by-Step Solution **Step 1: Simplifying \( f(x) \)** We start by simplifying \( f(x) \): \[ ...
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