How do you find the zeroes of #f (x) =x^6 − 64#?
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To find the zeroes of ( f(x) = x^6  64 ), set the function equal to zero and solve for (x):
[ x^6  64 = 0 ]
To solve this equation, we can use the difference of squares formula: (a^2  b^2 = (a + b)(a  b)). In this case, (a^2 = x^6) and (b^2 = 64), so:
[ x^6  64 = (x^3)^2  8^2 ]
Applying the difference of squares formula:
[ (x^3 + 8)(x^3  8) = 0 ]
Now we have two factors:
 ( x^3 + 8 = 0 )
 ( x^3  8 = 0 )
Solve each equation separately:

( x^3 + 8 = 0 ) Subtract 8 from both sides: ( x^3 = 8 ) Take the cube root of both sides: ( x = 2 )

( x^3  8 = 0 ) Add 8 to both sides: ( x^3 = 8 ) Take the cube root of both sides: ( x = 2 )
Therefore, the zeroes of ( f(x) = x^6  64 ) are ( x = 2 ) and ( x = 2 ).
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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.
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