How do you find f(g(x)), f(f(x)), g(g(x)), g(f(x)), given #f(x) = x^2# and #g(x) = ln(x) #?
To find ( f(g(x)) ), ( f(f(x)) ), ( g(g(x)) ), and ( g(f(x)) ) given ( f(x) = x^2 ) and ( g(x) = \ln(x) ):

( f(g(x)) ): Substitute ( g(x) ) into ( f(x) ): ( f(g(x)) = (ln(x))^2 ).

( f(f(x)) ): Substitute ( f(x) ) into ( f(x) ): ( f(f(x)) = (x^2)^2 = x^4 ).

( g(g(x)) ): Substitute ( g(x) ) into ( g(x) ): ( g(g(x)) = \ln(\ln(x)) ).

( g(f(x)) ): Substitute ( f(x) ) into ( g(x) ): ( g(f(x)) = \ln(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.
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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