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lets-f-R-R-and-g-R-R-two-continuous-and-differentiable-functions-suppose-that-g-0-0-then-compute-h-x-lim-x-0-g-f-x-x-f-x-x-




Question Number 1375 by 123456 last updated on 26/Jul/15
lets f:R→R and g:R→R two continuous and differentiable functions  suppose that g(0)=0, then compute  h(x)=lim_(Δx→0)  ((g(f(x+Δx)−f(x)))/(Δx))
$$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{and}\:{g}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{two}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differentiable}\:\mathrm{functions} \\ $$$$\mathrm{suppose}\:\mathrm{that}\:{g}\left(\mathrm{0}\right)=\mathrm{0},\:\mathrm{then}\:\mathrm{compute} \\ $$$${h}\left({x}\right)=\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{g}\left({f}\left({x}+\Delta{x}\right)−{f}\left({x}\right)\right)}{\Delta{x}} \\ $$

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