How do you integrate #int cos x / ((sin x)^(1/2))dx#?
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To integrate ( \frac{\cos(x)}{\sqrt{\sin(x)}} ) with respect to ( x ), you can use the substitution method.
Let: [ u = \sqrt{\sin(x)} ] [ \Rightarrow u^2 = \sin(x) ] [ \Rightarrow 2u , du = \cos(x) , dx ]
Substituting these values into the integral: [ \int \frac{\cos(x)}{\sqrt{\sin(x)}} , dx = \int \frac{2u , du}{u} ]
Simplifying: [ \int 2 , du = 2u + C ]
Substituting back for ( u ): [ = 2\sqrt{\sin(x)} + C ]
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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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