# How do you find the equation of a line tangent to the function #y=-2tanx# at (-pi,0)?

The equation of the line is

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To find the equation of a line tangent to the function y = -2tan(x) at (-π, 0), we need to determine the slope of the tangent line at that point.

The derivative of the function y = -2tan(x) can be found using the chain rule. The derivative of tan(x) is sec^2(x), and when multiplied by the constant -2, it becomes -2sec^2(x).

Substituting x = -π into the derivative, we get -2sec^2(-π). Since sec^2(-π) is equal to 1, the slope of the tangent line at (-π, 0) is -2.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values (-π, 0) and -2 into the equation.

Thus, the equation of the line tangent to the function y = -2tan(x) at (-π, 0) is y - 0 = -2(x - (-π)). Simplifying this equation gives y = -2x - 2π.

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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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