# How do you find the equation of the tangent line to the curve #y=secx# at #(pi/3,2)#?

(This is really just the point-slope form of a line in disguise!)

Now, we need to just plug in all of these values to give us the tangent line equation:

Or if the problem prefers slope intercept form:

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To find the equation of the tangent line to the curve y=secx at (pi/3,2), we need to find the derivative of the function y=secx and evaluate it at x=pi/3. The derivative of y=secx is dy/dx = secx * tanx. Evaluating this at x=pi/3, we get dy/dx = sec(pi/3) * tan(pi/3). Simplifying this, we have dy/dx = 2 * sqrt(3).

Now, we have the slope of the tangent line, which is dy/dx = 2 * sqrt(3). To find the equation of the tangent line, we use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (pi/3, 2) and m is the slope. Plugging in the values, we have y - 2 = (2 * sqrt(3))(x - pi/3). Simplifying this equation gives the equation of the tangent line to the curve y=secx at (pi/3,2).

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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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