Let f : R → R be a continuously differentiable function such that f(2) = 6 and \({\rm{f'}}\left( 2 \right) = \frac{1}{{48}}\). If \(\mathop \smallint \nolimits_6^{{\rm{f}}\left( {\rm{x}} \right)} \left( {4{{\rm{t}}^3}} \right){\rm{dt}} = \left( {{\rm{x}} - 2} \right){\rm{g}}\left( {\rm{x}} \right),{\rm{\;then\;}}\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 2} {\rm{\;g}}\left( {\rm{x}} \right)\) is equal to:

Let f : R → R be a continuously differentiable function such that f(

1.	Let f : R → R be a continuously differentiable function such that f(2) = 6 and \({\rm{f'}}\left( 2 \right) = \frac{1}{{48}}\). If \(\mathop \smallint \nolimits_6^{{\rm{f}}\left( {\rm{x}} \right)} \left( {4{{\rm{t}}^3}} \right){\rm{dt}} = \left( {{\rm{x}} - 2} \right){\rm{g}}\left( {\rm{x}} \right),{\rm{\;then\;}}\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 2} {\rm{\;g}}\left( {\rm{x}} \right)\) is equal to:
A.	18
B.	24
C.	12
D.	36
Answer» B. 24

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