# How do you find the equation of the tangent line of the function #f(x) = sin(2x)# when given the point (#pi,0#)?

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How do you find the equation of the tangent line of the function #f(x) = sin(2x)# when given the point (#pi,0# )?

How do you find the equation of the tangent line of the function

The tangent line of a curve

As we are given

Using that

#=cos(2x)(d/dx2x)#

#=2cos(2x)#

Thus

Plugging this into our equation for the tangent line, we get

Graphed together:

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To find the equation of the tangent line of the function f(x) = sin(2x) at the point (pi,0), we need to find the derivative of the function and then use the point-slope form of a line.

The derivative of f(x) = sin(2x) can be found using the chain rule. The derivative is f'(x) = 2cos(2x).

Now, we can find the slope of the tangent line at the point (pi,0) by substituting x = pi into the derivative. The slope is f'(pi) = 2cos(2pi) = 2cos(0) = 2.

Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values to find the equation of the tangent line.

Substituting (pi,0) and m = 2 into the point-slope form, we get y - 0 = 2(x - pi).

Simplifying the equation, we have y = 2x - 2pi.

Therefore, the equation of the tangent line of the function f(x) = sin(2x) at the point (pi,0) is y = 2x - 2pi.

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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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