Solve for #f(x)# the integral equation #int_1^xf(t)dt=x(f(x))^2# ?
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To solve the integral equation (\int_1^x f(t) , dt = x(f(x))^2):

Differentiate both sides of the equation with respect to (x).

Apply the Fundamental Theorem of Calculus to the left side to obtain (f(x)).

Solve for (f(x)) by equating the expressions obtained in steps 1 and 2.

Check for any additional solutions or restrictions on the domain of (f(x)).
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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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