(1 point) Let f(x)=(9)/(4pi -8x) Then the slope of the tangent : line to the graph of y=f(x) at the point (pi ,-(9)/(4pi )) is the limit as x tends to 3.14 of the following expression square The value of this limit is square It follows that the equation of the tangent line is y= square

To find the slope of the tangent line to the graph of at the point , we need to find the derivative of and evaluate it at .The derivative of is given by: f'(x) = \frac{d}{dx}\left(\frac{9}{4\pi - 8x}\right) Using the quotient rule, we have: f'(x) = \frac{9 \cdot (-8)}{(4\pi - 8x)^2} = \frac{-72}{(4\pi - 8x)^2} Now, we can evaluate at : f'(\pi) = \frac{-72}{(4\pi - 8\pi)^2} = \frac{-72}{(-4\pi)^2} = \frac{-72}{16\pi^2} = \frac{-9}{4\pi^2} Therefore, the slope of the tangent line to the graph of at the point is .Next, we need to find the value of the limit as tends to of the expression .Substituting and , we have: \lim_{x \to \pi} \frac{f(x) - f(\pi)}{x - \pi} = \lim_{x \to \pi} \frac{\frac{9}{4\pi - 8x} + \frac{9}{4\pi}}{x - \pi} Simplifying the expression, we get: \lim_{x \to \pi} \frac{9}{(4\pi - 8x)(4\pi)} \cdot \frac{4\pi}{x - \pi} = \lim_{x \to \pi} \frac{9}{(4\pi - 8x)(4\pi)(x - \pi)} As approaches , the denominator approaches zero, so the limit is undefined.Therefore, the value of the limit is undefined.Finally, we can use the point-slope form of a linear equation to find the equation of the tangent line: y - y_1 = m(x - x_1) Substituting , , and , we have: y + \frac{9}{4\pi} = \frac{-9}{4\pi^2}(x - \pi) Simplifying the equation, we get: y = \frac{-9}{4\pi^2}(x - \pi) - \frac{9}{4\pi} Therefore, the equation of the tangent line is .