# What is the slope of the polar curve #f(theta) = theta^2-theta - cos^3theta + tan^2theta# at #theta = pi/3#?

The slope,

Slope of a tangent to a polar curve

From the reference we have the equation:

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To find the slope of the polar curve at a specific point, you can first compute the derivative of the polar function with respect to theta and then evaluate it at the given theta value.

The derivative of the polar function f(theta) = theta^2 - theta - cos^3(theta) + tan^2(theta) with respect to theta is given by:

f'(theta) = 2theta - 1 + 3cos^2(theta)sin(theta) + 2tan(theta)sec^2(theta)

Now, you can plug in theta = pi/3 into this derivative expression and calculate the value to find the slope of the curve at theta = 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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