How do you find the parametric equations for the line through the point P = (4, 4, 1) that is perpendicular to the plane 3x + 1y  4z = 1?
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To find the parametric equations for the line through point P = (4, 4, 1) perpendicular to the plane 3x + y  4z = 1, follow these steps:

Find the normal vector to the plane by extracting the coefficients of x, y, and z from the plane equation: (3, 1, 4).

Let's call the direction vector of the line we seek D. Since the line is perpendicular to the plane, the direction vector D should be parallel to the normal vector of the plane. Therefore, D = (3, 1, 4).

Now, to find a point on the line, use the given point P = (4, 4, 1).

The parametric equations of the line can be written as: x = 4 + 3t y = 4 + t z = 1  4t
These equations represent all the points (x, y, z) on the line, where t is a parameter that can take any real value.
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When evaluating a onesided 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 onesided 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 onesided 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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