# How do you find the equation of the line tangent to #y=cosx# at x=π/4?

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To find the equation of the line tangent to y=cosx at x=π/4, we need to find the derivative of the function y=cosx and evaluate it at x=π/4. The derivative of y=cosx is dy/dx = -sinx. Evaluating this at x=π/4, we get dy/dx = -sin(π/4) = -√2/2.

The slope of the tangent line is equal to the derivative at the given point, so the slope of the tangent line is -√2/2.

To find the equation of the line, we use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point on the line and m is the slope. Plugging in the values x1=π/4, y1=cos(π/4) = √2/2, and m=-√2/2, we get the equation of the tangent line as y - √2/2 = -√2/2(x - π/4).

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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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