How do you find the limit of # [cos(x+(pi/2))]/[cos(x-(pi/2))]# as x approaches pi?
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To find the limit of [cos(x+(pi/2))]/[cos(x-(pi/2))] as x approaches pi, we can use the limit properties and trigonometric identities.
First, let's simplify the expression using the cosine addition and subtraction formulas:
cos(x + (pi/2)) = cos(x)cos(pi/2) - sin(x)sin(pi/2) = -sin(x) cos(x - (pi/2)) = cos(x)cos(pi/2) + sin(x)sin(pi/2) = sin(x)
Now, we can rewrite the expression as:
[-sin(x)] / [sin(x)]
Since sin(x) is not equal to zero when x approaches pi, we can cancel out the sin(x) terms:
-1
Therefore, the limit of [cos(x+(pi/2))]/[cos(x-(pi/2))] as x approaches pi is -1.
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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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