How do you write the cartesian equation for #r=13cosx#?
As below
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To write the Cartesian equation for ( r = 1  3 \cos(x) ), where ( r ) represents the distance from the origin to a point ( (x, y) ) in polar coordinates, follow these steps:

Use the relationship between polar coordinates ( (r, \theta) ) and Cartesian coordinates ( (x, y) ): [ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

Substitute the given polar equation ( r = 1  3 \cos(x) ) into the expression for ( x ) and ( y ): [ x = (1  3 \cos(x)) \cos(\theta) ] [ y = (1  3 \cos(x)) \sin(\theta) ]

Since ( \theta ) is not specified in the equation, you may express ( x ) and ( y ) solely in terms of ( x ) and ( y ): [ x = (1  3 \cos(x)) \frac{x}{r} ] [ y = (1  3 \cos(x)) \frac{y}{r} ]

Substitute ( r = \sqrt{x^2 + y^2} ) into the expressions for ( x ) and ( y ): [ x = (1  3 \cos(x)) \frac{x}{\sqrt{x^2 + y^2}} ] [ y = (1  3 \cos(x)) \frac{y}{\sqrt{x^2 + y^2}} ]

Clear the denominators by multiplying both sides by ( \sqrt{x^2 + y^2} ): [ x \sqrt{x^2 + y^2} = (1  3 \cos(x))x ] [ y \sqrt{x^2 + y^2} = (1  3 \cos(x))y ]

Square both sides of the equations to eliminate the square roots: [ x^2 (x^2 + y^2) = (1  3 \cos(x))^2 x^2 ] [ y^2 (x^2 + y^2) = (1  3 \cos(x))^2 y^2 ]

Simplify the expressions to obtain the Cartesian equation in terms of ( x ) and ( y ).
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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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