108Fall12Ex1VersionASolutions

# 1 3 pts bounded by y x 1 and the x and y axes

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Unformatted text preview: 5 x + C 2 d) *** 1 x2 5 + C ln 5 3 MthSc 108 Test 1-Version A Fall 2012 10. (3 pts.) Express 3 ln ( cos x ) − ln x 2 + 1 + ( ln 4 ) log 4 ( 3x ) as a natural logarithm of a single ( ) quantity. ( ) a) ln 3 cos x − ( x 2 + 2 ) + 12 x ⎛ ( 3x )ln 4 cos 3 x ⎞ c) ln ⎜ x2 + 1 ⎟ ⎝ ⎠ ⎛ cos 3 x ⎞ b) ln ⎜ 3x + 2 x +1⎟ ⎝ ⎠ ⎛ 3x cos 3 x ⎞ d)*** ln ⎜ 2 ⎝ x + 1 ⎟ ⎠ 11. −1 (3 pts.) Find the slope of the line tangent to f ( x ) = sec ( 3x ) when x = 1 . 1 10 a) b) *** 1 8 3 c) 8 d) It is not defined. Which integral gives the correct volume when the region bounded by the x- axis, 12. (3 pts.) f ( x ), g ( x ), and h( x ) is rotated about the y- axis? b a) ∫ 2π xh( x ) dx b b) *** ∫ 2π xf ( x ) dx + ∫ 2π xh( x ) dx a d a d c 0 f f c) ∫ 2π xf ( x ) dx + ∫ 2π xh( x ) dx b d) ∫ π [ h( x )] dx 2 a 4 MthSc 108 Test 1-Version A Fall 201...
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