How do you find the asymptotes for #y= 1/2 sec x#?
x = an odd multiple of
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To find the asymptotes of the function ( y = \frac{1}{2} \sec(x) ), we need to consider the properties of the secant function. Secant has vertical asymptotes where its cosine counterpart, cosine, equals zero. Thus, the vertical asymptotes occur at points where ( \cos(x) = 0 ). The cosine function equals zero at odd multiples of ( \frac{\pi}{2} ). Therefore, the vertical asymptotes of ( y = \frac{1}{2} \sec(x) ) occur at ( x = (2n + 1) \frac{\pi}{2} ), where ( n ) is an integer.
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To find the asymptotes for the function ( y = \frac{1}{2} \sec(x) ), follow these steps:

Vertical asymptotes:
 Vertical asymptotes occur where the denominator of the secant function becomes zero.
 Secant function has vertical asymptotes at odd multiples of ( \frac{\pi}{2} ), i.e., ( x = \frac{\pi}{2} + k\pi ) where ( k ) is an integer.

Horizontal asymptotes:
 Horizontal asymptotes occur when the function approaches a constant value as ( x ) approaches positive or negative infinity.
 Since secant oscillates between ( \infty ) and ( +\infty ), there are no horizontal asymptotes.
Therefore, the vertical asymptotes for ( y = \frac{1}{2} \sec(x) ) occur at ( x = \frac{\pi}{2} + k\pi ) where ( k ) is an integer, and there are no horizontal asymptotes.
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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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