# How do you find the equation of the tangent line to the curve #f(x)= x + cos (x)# at x = 0?

Equation of tangent line is

Hence, equation of tangent line is

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To find the equation of the tangent line to the curve f(x) = x + cos(x) at x = 0, we need to find the slope of the tangent line at that point and then use the point-slope form of a line to write the equation.

To find the slope, we take the derivative of f(x) with respect to x. The derivative of x is 1, and the derivative of cos(x) is -sin(x). Therefore, the derivative of f(x) is 1 - sin(x).

Plugging in x = 0 into the derivative, we get 1 - sin(0) = 1 - 0 = 1. So, the slope of the tangent line at x = 0 is 1.

Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute x1 = 0, y1 = f(0) = 0 + cos(0) = 1 into the equation.

Therefore, the equation of the tangent line to the curve f(x) = x + cos(x) at x = 0 is y - 1 = 1(x - 0), which simplifies to y = x + 1.

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