APPM 1350 Midterm: appm1350fall2017exam4_sol
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Fall 2017: (26 pts) evaluate the following. (a) let g(x) = cos3( 2x). Find g ( /3). (b) let y = ( x)x e 1/r ln(r) (c) Solution: (a) (9 pt) g (x) = 3 cos2( 2x)( sin( 2x))( 2) = 6 cos2( 2x) sin( 2x) g ( /3) = 6 cos2( /3) sin( /3) = 6(cid:0) 1 (b) (9 pt) use logarithmic differentiation. =(cid:0) x(cid:1)x(cid:18) 1 ln x(cid:19) ln 4(cid:19) = 8(1 + ln 4) = 8(1 + 2 ln 2) y (4) =(cid:0)24(cid:1)(cid:18) 1 dy dx dy dx ln x = ln x. 2 ln r e1/r (c) (8 pt) lim r 0+ e 1/r ln(r) = lim r 0+ = 0 because the numerator approaches 0 and the denominator approaches as r 0+: (24 pts) evaluate the following integrals. (a) z 3x3 + 5x + 7 x2 dx.
