How do you find the general solution to #dy/dx=1/sec^2y#?
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To find the general solution to the differential equation (\frac{dy}{dx} = \frac{1}{\sec^2 y}), you would follow these steps:

Rewrite the equation using trigonometric identities: (\frac{dy}{dx} = \cos^2 y).

Separate variables: (\frac{dy}{\cos^2 y} = dx).

Integrate both sides: (\int \frac{dy}{\cos^2 y} = \int dx).

The integral of (\frac{1}{\cos^2 y}) with respect to (y) is (\tan y): (\tan y = x + C), where (C) is the constant of integration.
So, the general solution to the differential equation is: [ \tan y = x + C ]
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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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