# How do you find an equation to the tangent line to the curve #y = 2 sin^2x# at #x = Pi/4#?

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To find the equation of the tangent line to the curve y = 2 sin^2x at x = Pi/4, we need to find the slope of the tangent line and a point on the line.

First, find the derivative of the function y = 2 sin^2x using the chain rule: dy/dx = 2 * 2 sin(x) * cos(x) = 4 sin(x) cos(x)

Evaluate the derivative at x = Pi/4: dy/dx = 4 sin(Pi/4) cos(Pi/4) = 4 * (1/sqrt(2)) * (1/sqrt(2)) = 4/2 = 2

The slope of the tangent line is 2.

Next, find the y-coordinate of the point on the curve at x = Pi/4: y = 2 sin^2(Pi/4) = 2 * (1/2)^2 = 2 * 1/4 = 1/2

The point on the curve is (Pi/4, 1/2).

Using the point-slope form of a line, the equation of the tangent line is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line.

Plugging in the values, we get: y - 1/2 = 2(x - Pi/4)

Simplifying the equation gives the equation of the tangent line: y = 2x - Pi/2 + 1/2

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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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