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高数题,求解答,谢谢
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1)lim(y→0+)F(x,y)
= lim(y→0+)∫[-y,y]f(x+t)dt/(2y) (0/0)
= lim(y→0+)[f(x+y)-f(x-y)(-1)]/2
= f(x);
2)DF/Dx
= (D/Dx){∫[-y,y]f(x+t)dt/(2y)}
= ∫[-y,y]f'(x+t)dt/(2y)
= [f(x+y)-f(x-y)]/(2y);
3)lim(y→0+)(DF/Dx)
= lim(y→0+)[f(x+y)-f(x-y)]/(2y) (0/0)
= lim(y→0+)[f'(x+y)-f'(x-y)(-1)]/2
= f'(x)。
= lim(y→0+)∫[-y,y]f(x+t)dt/(2y) (0/0)
= lim(y→0+)[f(x+y)-f(x-y)(-1)]/2
= f(x);
2)DF/Dx
= (D/Dx){∫[-y,y]f(x+t)dt/(2y)}
= ∫[-y,y]f'(x+t)dt/(2y)
= [f(x+y)-f(x-y)]/(2y);
3)lim(y→0+)(DF/Dx)
= lim(y→0+)[f(x+y)-f(x-y)]/(2y) (0/0)
= lim(y→0+)[f'(x+y)-f'(x-y)(-1)]/2
= f'(x)。
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谢谢你^_^
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