导数的初级问题,设函数F(X)可导,则LIM [F(1+ ΔX)-F(1)]/3 ΔX 等于?A.F'(1) B.3F'(1) C.1/3F'(1) D.F'(3) 麻烦给下过程,稍后把分补上
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![导数的初级问题,设函数F(X)可导,则LIM [F(1+ ΔX)-F(1)]/3 ΔX 等于?A.F'(1) B.3F'(1) C.1/3F'(1) D.F'(3) 麻烦给下过程,稍后把分补上](/uploads/image/z/7840406-38-6.jpg?t=%E5%AF%BC%E6%95%B0%E7%9A%84%E5%88%9D%E7%BA%A7%E9%97%AE%E9%A2%98%2C%E8%AE%BE%E5%87%BD%E6%95%B0F%28X%29%E5%8F%AF%E5%AF%BC%2C%E5%88%99LIM+%5BF%281%2B+%CE%94X%29-F%281%29%5D%2F3+%CE%94X+%E7%AD%89%E4%BA%8E%3FA.F%27%281%29+B.3F%27%281%29+C.1%2F3F%27%281%29+D.F%27%283%29+%E9%BA%BB%E7%83%A6%E7%BB%99%E4%B8%8B%E8%BF%87%E7%A8%8B%2C%E7%A8%8D%E5%90%8E%E6%8A%8A%E5%88%86%E8%A1%A5%E4%B8%8A)
导数的初级问题,设函数F(X)可导,则LIM [F(1+ ΔX)-F(1)]/3 ΔX 等于?A.F'(1) B.3F'(1) C.1/3F'(1) D.F'(3) 麻烦给下过程,稍后把分补上
导数的初级问题,
设函数F(X)可导,则LIM [F(1+ ΔX)-F(1)]/3 ΔX 等于?
A.F'(1) B.3F'(1) C.1/3F'(1) D.F'(3)
麻烦给下过程,稍后把分补上
导数的初级问题,设函数F(X)可导,则LIM [F(1+ ΔX)-F(1)]/3 ΔX 等于?A.F'(1) B.3F'(1) C.1/3F'(1) D.F'(3) 麻烦给下过程,稍后把分补上
选C
根据导数的公式可得LIM [F(X+ ΔX)-F(X)]/ΔX = F'(X)
当X=1时,LIM [F(1+ ΔX)-F(1)]/ΔX = F'(1)
所以,LIM [F(1+ ΔX)-F(1)]/3 ΔX
=(1/3)LIM [F(1+ ΔX)-F(1)]/ΔX
=1/3F'(1)
LIM [F(1+ ΔX)-F(1)]/3 ΔX =1/3 LIM [F(1+ ΔX)-F(1)]/ ΔX =1/3F'(1)