Question

这题求解 谢谢。

Answer 1

Answer 2

lim(x->2) (x^2-3x+2)/(x^2-4)
=lim(x->2) (x-1)(x-2)/[(x-2)(x+2)]
=lim(x->2) (x-1)/(x+2)
=(2-1)/(2+2)
=1/4
∫(0->ln2) e^x.(4+e^x)^2 dx
=∫(0->ln2) (4+e^x)^2 d(4+e^x)
=(1/3)[(4+e^x)^3]|(0->ln2)
=(1/3)( 6^3 - 5^3)
=91/3
∫(1->e) (1+5lnx)/x dx
=∫(1->e) (1/x) dx +5∫(1->e) (lnx/x) dx
=[lnx]|(1->e) +5∫(1->e) lnx dlnx
=1 +(5/2)[(lnx)^2]|(1->e)
=1 +5/2
=7/2
∫(0->π/2) xsinx dx
=-∫(0->π/2) xdcosx
=-[xcosx]|(0->π/2) +∫(0->π/2) cosx dx
=0 +[sinx]|(0->π/2)
=1
Part 2
=77{ 4.[lim(x->2) (x^2-3x+2)/(x^2-4)] +3∫(0->ln2) e^x.(4+e^x)^2 dx
+2∫(1->e) (1+5lnx)/x dx +∫(0->π/2) xsinx dx}
=77( 1 +91 +7 +1 )
=77(100)
=7700