# How do you find the equation for the tangent line to #sec^2x# at #x=pi/3#?

Equation of tangent is

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To find the equation for the tangent line to sec^2x at x=pi/3, we need to find the derivative of sec^2x and evaluate it at x=pi/3.

The derivative of sec^2x can be found using the chain rule.

The derivative of sec^2x is 2sec^2x * tanx.

Evaluating this derivative at x=pi/3, we have:

2sec^2(pi/3) * tan(pi/3).

Using the trigonometric identities, sec(pi/3) = 2 and tan(pi/3) = sqrt(3), we can simplify the equation to:

2(2)^2 * sqrt(3) = 8sqrt(3).

Therefore, the equation for the tangent line to sec^2x at x=pi/3 is y = 8sqrt(3)(x - pi/3) + sec^2(pi/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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