Let f(x)=3×10-7×8+5×6-21×3+3×2-7.The value of limh→0f(1-h)-f(1)h3+3h is

Let $f (x) = 3 x^{10} - 7 x^{8} + 5 x^{6} - 21 x^{3} + 3 x^{2} - 7$ .The value of $\lim_{h \to 0} \frac{f (1 - h) - f (1)}{h^{3} + 3 h}$ is

A
50/3
B
22/3
C
13
D
53/3

Solution:

$= \lim_{h \to 0} \frac{f (1 - h) - f (1)}{h^{3} + 3 h}$

$= \lim_{h \to 0} \frac{f (1 - h) - f (1)}{- h} \cdot \frac{- 1}{h^{2} + 3}$

$= f^{'} (1) (- 1 / 3) = 53 / 3$ .

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