How do you differentiate the following parametric equation: # x(t)=cost, y(t)=sint #?
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To differentiate the parametric equations x(t) = cos(t) and y(t) = sin(t) with respect to t, you simply differentiate each equation separately using the chain rule if necessary.
The derivative of x(t) = cos(t) with respect to t is dx/dt = -sin(t), and the derivative of y(t) = sin(t) with respect to t is dy/dt = cos(t).
So, the parametric differentiation results are: dx/dt = -sin(t), dy/dt = cos(t).
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To differentiate the parametric equations (x(t) = \cos(t)) and (y(t) = \sin(t)) with respect to (t), you can use the chain rule. The chain rule states that if (y = f(u)) and (u = g(x)), then (\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}).
In this case, (x = \cos(t)) and (y = \sin(t)), so we have (x = f(t)) and (y = g(t)). Differentiating (x) and (y) with respect to (t) gives:
[\frac{dx}{dt} = -\sin(t)] [\frac{dy}{dt} = \cos(t)]
These are the derivatives of (x) and (y) with respect to (t), respectively.
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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.
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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