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**pratique21** Hi!

Fir the first one you need to apple L'Hospital recursively until you rid the 'x' term in the denominator

(e^{x} - (1+x)) / x^{n}

so differentiate to get

(e^{x} - 1 ) / n * x^{n-1}

Repeat

(e^{x}) / n(n-1) * x^{n-2}

So now you know that if you keep differentiating, the numerator remains unaffected. However the denominator will reduce to something like

(n)(n-1)(n-2)......1 (= say N)

Now put the limiting value of x=0

you get

1/ N

Regarding the second one, i think the left hand limit will come out to be 0. Since the domain of the function is (-inf,5] , the LHL exists as x->5-

Hope it helps !