mcastillo356
Gold Member
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- TL;DR
- I think there is a typo in this demo
Hi, PF, I think I've found a typo in my textbook. It says:
"In the case of a multiplication by a constant, we've got
$$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$"
My opinion: it should be
$$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=C\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$
Greetings!
"In the case of a multiplication by a constant, we've got
$$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$"
My opinion: it should be
$$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=C\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$
Greetings!