let f(x)= (√(2+x^2 )) −x
1) calculate lim_(x→+∞) f(x) and lim_(x→−∞) f(x)
2) calculate lim_(x→+∞) ((f(x))/x) and lim_(x→−∞) ((f(x))/x)
3) calculate f^′ (x) and determine its sign
4) give the variation of
5) give the equation of assymptote at point
A(1,f(1))
6) find f^(−1) (x) and calculate (f^(−1) )^′ (x)
7) calculate ∫_0 ^4 f(x)dx .
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