Unformatted text preview: 2 and y = 4. Find the volume of the solid given that cross sections perpendicular to the y axis are equilateral triangles. 2. Let R be the region bounded by the lines y = x , y = 2 x , and y = 4. Find the volume of the solid obtained by rotating R about the line y = 4. 3. Let f ( x ) = √ x 2 + 2 x , for x > 0. Show that f is one-to-one on the given domain and ﬁnd the inverse of f . 4. Use logarithmic diﬀerentiation to ﬁnd the derivative of f ( x ) = v u u t x 3 sin x (1-cos x )( x 2 + 1) . 5. Find the integrals: (a) Z dx x (ln x ) 2 . (b) Z 4 1 1 √ x (1 + √ x ) dx ....
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This note was uploaded on 11/30/2010 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas.
- Spring '06