# What is the equation of the tangent line of #f(x) =(4x) / (3-4x^2-x) # at # x = 1#?

Let's use the quotient rule to determine the first derivative:

Finally,

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To find the equation of the tangent line of f(x) at x = 1, we need to find the slope of the tangent line and a point on the line.

First, we find the derivative of f(x) using the quotient rule:

f'(x) = [(3-4x^2-x)(4) - (4x)(-8x-1)] / (3-4x^2-x)^2

Next, we substitute x = 1 into f'(x) to find the slope of the tangent line at x = 1:

f'(1) = [(3-4(1)^2-1)(4) - (4(1))(-8(1)-1)] / (3-4(1)^2-1)^2

Finally, we substitute the slope and the point (1, f(1)) into the point-slope form of a line to find the equation of the tangent line.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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