PracticeFinal - r 8 Evaluate the integral Z 9 1 √ u-2 u 2...

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Math141 - Practice Final 1. (a): Find the exact value of sin(cos - 1 4 5 ). (b): Find the exact value of log 2 6 - log 2 15 + log 2 20. 2. Find an equation of the tangent and normal line to the curve y = 2 x x +1 at the point (1 , 1). 3. Calculate y 0 y = (4 x - x 2 ) 100 y = e sin 2 2 θ y = x sin x cos( xy ) = x 2 - y y = (cos x ) x y = ( x 2 + 1) 4 (2 x + 1) 3 (3 x - 1) 5 y = arctan(arcsin x ) y = e 1 /x x 2 4. A cylindrical tank with radius 5m is being filled with water at a rate of 3m 3 / min. How fast is the height of the water increasing? 5. Find the absolute maximum and minimum values of the functions on the given interval, f ( t ) = 2 cos t + sin 2 t, [0 , π/ 2] f ( t ) = t 4 - t 2 , [ - 1 , 2] 6. Find the limits. lim h 0 1 + h - 1 h ; lim x →-∞ x 2 - 9 2 x - 6 ; 1
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lim x 0 1 - cos x x 2 ; lim x →∞ x 3 e - x 2 ; lim x 0 + ( x ) x 2 . 7. Find the area of the largest rectangle that can be inscribed in a semicircle of radius
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Unformatted text preview: r . 8. Evaluate the integral. Z 9 1 √ u-2 u 2 u du ; Z 2 x (2 + x 5 ) dx ; Z cos θ sin 6 θdθ Z 1 (1-x ) 9 dx ; Z e 4 e dx x √ ln x dx ; Z 1 e x 1 + e 2 x dx ; Z x + 2 √ x 2 + 4 x dx. 9. Find the area of the region enclosed by the given cures y = x 2 ,y = 4 x-x 2 x + y = 0 ,x = y 2 + 3 y 10. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 2 x,y = x 2 ; about the x-axis x = 0 ,x = 9-y 2 ; about x =-1 2...
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