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Question Number 96607 Answers: 0 Comments: 1

It is given that f(x) is a function defined on R, satisfying f(1)=1 and for any x∈R, f(x+5) ≥f(x)+5 and f(x+1) ≤f(x)+1. If g(x)= f(x)+1−x, then g(2002) = ___

$$\mathrm{It}\:\mathrm{is}\:\mathrm{given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{function} \\ $$$$\mathrm{defined}\:\mathrm{on}\:\mathbb{R},\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{for}\:\mathrm{any}\:\mathrm{x}\in\mathbb{R},\:\mathrm{f}\left(\mathrm{x}+\mathrm{5}\right)\:\geqslant\mathrm{f}\left(\mathrm{x}\right)+\mathrm{5} \\ $$$$\mathrm{and}\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)\:\leqslant\mathrm{f}\left(\mathrm{x}\right)+\mathrm{1}.\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)= \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{1}−\mathrm{x},\:\mathrm{then}\:\mathrm{g}\left(\mathrm{2002}\right)\:=\:\_\_\_ \\ $$

Question Number 96606 Answers: 0 Comments: 1

Question Number 96604 Answers: 0 Comments: 6

Please how will you evaluate ∫ (√dx) ???

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{will}\:\mathrm{you}\:\mathrm{evaluate} \\ $$$$\:\int\:\sqrt{{dx}}\:??? \\ $$

Question Number 96602 Answers: 3 Comments: 0

lim_(n→+∞) (1/(√n)) Σ_(k=1) ^n (√k)

$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\sqrt{\mathrm{n}}}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{k}} \\ $$

Question Number 96593 Answers: 2 Comments: 0

let f(x) =arctan(x^n ) with n integr natural 1) calculate f^′ (x) and f^((2)) (x) 2) calculate f^((n)) (x) and f^((n)) (0) 3)developp f at integr serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arctan}\left(\mathrm{x}^{\mathrm{n}} \right)\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{'} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{2}\right)} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$

Question Number 96596 Answers: 2 Comments: 0

x(x+1) (dy/dx)−(2x+1)y = 0

$${x}\left({x}+\mathrm{1}\right)\:\frac{{dy}}{{dx}}−\left(\mathrm{2}{x}+\mathrm{1}\right){y}\:=\:\mathrm{0} \\ $$

Question Number 96595 Answers: 0 Comments: 0

∫_0 ^1 x^(4035) (x^4 +1)^(2017) (3x+1)^4 dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{4035}} \left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2017}} \left(\mathrm{3}{x}+\mathrm{1}\right)^{\mathrm{4}} {dx} \\ $$

Question Number 96586 Answers: 1 Comments: 0

find the minimum value of f(x)=x^x for x∈R^+

$${find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)={x}^{{x}} \\ $$$${for}\:{x}\in\mathbb{R}^{+} \\ $$

Question Number 96584 Answers: 1 Comments: 4