y=e⁻⁴ˣ/x
eˣ=1+x/1!+x/2!+x²/3!+x³/4!+x⁴/5!+...+xⁿ/n!.
y(0)=1/x.
y(1)=-4x/(x*1!)=-4.
y(2)=(-4x)²/(x*2!)=16x²/2x=8x.
y(3)=(-4x)³/(x*3!)=-64x³/6x=-32x²/3.
y(4)=(-4x)⁴/(x*4!)=256x⁴/24x=32x³/3.
y(5)=(-4x)⁵/(x*5!)=-1024x⁵/120x=-128x⁴/15.
y(6)=(-4x)⁶/(x*6!)=4096x⁶/720x=256x⁵/45. ⇒
Ответ: e⁻⁴ˣ/x=1/x-4+6x-32x²/3+32x³/3-128x⁴/15+256x⁵/45+...
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y=e⁻⁴ˣ/x
eˣ=1+x/1!+x/2!+x²/3!+x³/4!+x⁴/5!+...+xⁿ/n!.
y(0)=1/x.
y(1)=-4x/(x*1!)=-4.
y(2)=(-4x)²/(x*2!)=16x²/2x=8x.
y(3)=(-4x)³/(x*3!)=-64x³/6x=-32x²/3.
y(4)=(-4x)⁴/(x*4!)=256x⁴/24x=32x³/3.
y(5)=(-4x)⁵/(x*5!)=-1024x⁵/120x=-128x⁴/15.
y(6)=(-4x)⁶/(x*6!)=4096x⁶/720x=256x⁵/45. ⇒
Ответ: e⁻⁴ˣ/x=1/x-4+6x-32x²/3+32x³/3-128x⁴/15+256x⁵/45+...