lim x趋向0[e^(x^2)-e^(2-2cosx)]/x^4 答案是1/12

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lim x趋向0[e^(x^2)-e^(2-2cosx)]/x^4 答案是1/12
lim x趋向0[e^(x^2)-e^(2-2cosx)]/x^4 答案是1/12

lim x趋向0[e^(x^2)-e^(2-2cosx)]/x^4 答案是1/12
lim(x→0) [e^(x^2)-e^(2-2cosx)]/x^4
=lim(x→0) [e^(x^2)-e^2/e^(2cosx)]/x^4
=lim(x→0) [e^(x^2)*e^(2cosx)-e^2]/[e^(2cosx)*x^4]
=lim(x→0) [e^(x^2)*e^(2cosx)-e^2]/[e^2*x^4]
=lim(x→0) [e^(x^2+2cosx)-e^2]/[e^2*x^4] (0/0)
=lim(x→0) [e^(x^2+2cosx)*(2x-2sinx)]/[4e^2*x^3]
=lim(x→0) [e^2*(2x-2sinx)]/[4e^2*x^3]
=lim(x→0) (x-sinx)/[2x^3] (0/0)
=lim(x→0) (1-cosx)/(6x^2)
=lim(x→0) (x^2/2)/(6x^2)
=1/12

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