Math  /  Calculus

QuestionFind the limit as hh approaches 0 for the difference quotient of: 1. f(x)=x2xf(x)=x^{2}-x, 2. f(x)=1x+3f(x)=\frac{1}{x+3}.

Studdy Solution
Substitute h=0h=0 into the expression.
limh0f(x+h)f(x)h=(x+3)2\lim{h \rightarrow0} \frac{f(x+h)-f(x)}{h} = \frac{-}{(x+3)^{2}}The solution is limh0f(x+h)f(x)h=2x\lim{h \rightarrow0} \frac{f(x+h)-f(x)}{h} =2x - for f(x)=x2xf(x)=x^{2}-x and limh0f(x+h)f(x)h=(x+3)2\lim{h \rightarrow0} \frac{f(x+h)-f(x)}{h} = \frac{-}{(x+3)^{2}} for f(x)=x+3f(x)=\frac{}{x+3}.

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