Question

Let \(f(x)=3 x^{10}-7 x^{8}+5 x^{6}-21 x^{3}+3 x^{2}-7\). Then \(\lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{h^{3}+3 h}\)
(A) does not exsit
(B) is \(\frac{50}{3}\)
(C) is \(\frac{53}{3}\)
(D) is \(\frac{22}{3}\)

Answer 1

Ans: (C)
Hint \(: \lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{h^{3}+3 h}=\lim _{h \rightarrow 0} \frac{f(1)-f(1-h)}{-h} \times \frac{h}{h^{3}+3 h}\) \(=-f^{\prime}(1) \times \frac{1}{3}=\frac{53}{3}\)

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