# How do you find the equation of a line tangent to the function #y=-3/(x^2-4)# at (1, 1)?

We need to find the derivative of this function. This will allow us to find the gradient of the tangent line.

Notice we can write this as:

Using the chain rule:

Plugging in 1 will give us the gradient of the line.

We now have the gradient

equation of a line

Equation of line is:

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To find the equation of a line tangent to the function y = -3/(x^2-4) at (1, 1), we need to find the derivative of the function and evaluate it at x = 1.

First, let's find the derivative of y with respect to x using the quotient rule:

dy/dx = [(-3)(2x)] / (x^2-4)^2

Next, we substitute x = 1 into the derivative expression:

dy/dx = [(-3)(2(1))] / (1^2-4)^2 = -6 / (-3)^2 = -6 / 9 = -2/3

So, the slope of the tangent line at x = 1 is -2/3.

Now, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form is given by:

y - y1 = m(x - x1)

Substituting the values we have, (x1, y1) = (1, 1) and m = -2/3:

y - 1 = (-2/3)(x - 1)

Simplifying the equation:

y - 1 = (-2/3)x + 2/3

Finally, we can rewrite the equation in slope-intercept form:

y = (-2/3)x + 2/3 + 1 y = (-2/3)x + 5/3

Therefore, the equation of the line tangent to the function y = -3/(x^2-4) at (1, 1) is y = (-2/3)x + 5/3.

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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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