Page 57 - Math SL HB Sem 2

PAPER 2 (INTEGRATION)

I Letf (x)-- e'g -?\.

(a) Show thatl'(.x) = e' (t -U - l).
(3)

Part of the graph of y:.f (r), for - 6 < x 32, is shown below. The .r-coordinates of the local
minimum and maximum points are r and s respectively.

J

(b) Write down the equation ofthe horizontal asymptote.
(r)

(c) Write down the value of r and of s.
(4)

(d) Let I be the normal to the curve of/at P(0, l). Show that I has equation r +/: l.
(4)

(e) Let.R be the region enclosed by the curveT =;f(.t) and the line Z.

(D Find an expression for the area ofR.
(ii) Calculate the area ofR.
(s)
(Total l7 marks)

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