How do you graph the curve whose parametric equations are given and show its orientation given #x = sqrt{t} + 4#, #y = sqrt{t}  4#, where #t>=0#?
Pleasesee below.
graph{xy=8 [4, 24, 7, 3]}
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Plot Initial Points: Start by substituting various values of (t \geq 0) (like (t = 0, 1, 4, 9)) into the parametric equations (x = \sqrt{t} + 4) and (y = \sqrt{t}  4). Calculate the corresponding (x) and (y) values for these (t) values.

Graph Points and Curve:
 For (t = 0), (x = 4) and (y = 4).
 Increase (t) gradually. As (t) increases, both (x) and (y) increase since both are functions of (\sqrt{t}), but (x) will always be 8 units more than (y) due to their respective constants.
 Plot these points on the coordinate plane.

Orientation: The curve's orientation (direction of increasing (t)) starts from the point (4, 4) and moves upwards and to the right, as both (x) and (y) increase with (t).

Shape of the Curve: The curve will be a part of the graph where (x > 4) and (y > 4), showing a diagonal movement away from the origin as (t) increases, following the line (y = x  8), but with a curve that softens as it moves away from the point (4, 4) due to the square root function's decreasing rate of increase.

Drawing: On graph paper, plot the calculated points, draw the curve through these points, and indicate the orientation with an arrow showing the direction in which (t) increases.
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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.
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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