What is #f(x) = int 3x^2-4 dx# if #f(2) = 2 #?
First, find the antiderivative of the function using the product rule in reverse:
Thus,
Thus,
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To find ( f(x) = \int (3x^2 - 4) , dx ) if ( f(2) = 2 ), you first need to find the indefinite integral of ( 3x^2 - 4 ) with respect to ( x ), which is ( x^3 - 4x + C ), where ( C ) is the constant of integration. Then, evaluate ( f(x) ) at ( x = 2 ) and equate it to 2:
( f(2) = (2)^3 - 4(2) + C = 2 )
Solve for ( C ):
( 8 - 8 + C = 2 )
( C = 2 )
So, the integral ( f(x) ) is ( x^3 - 4x + 2 ).
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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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