pexam1 - Math 16B: Practice problems for Midterm 1 Note:...

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Math 16B: Practice problems for Midterm 1 Note: The midterm itself will not be this long. These are just some problems to get you ready. 1. Find the indefinite integral and check your answer by differentiation. (a) R 3 dx (b) R (5 x - 1) dx (c) R 1 x +3 dx (d) R (sin( x ) + x ) dx (e) R ( e x + 3) dx 2. Use substitution to find the indefinite inte- gral. (a) R x 2 2+ x 3 dx (g) R 1+ e x e x dx (b) R 3 x - 1 (3 x 2 - 2 x +1) 4 dx (h) R x +1 x 2 +2 x dx (c) R 3 x - 1 3 x 2 - 2 x +1 dx (i) R 1 x · ln( x ) dx (d) R x 2 2 - x 3 dx (j) R e x sin( e x ) dx (e) R cos 4 ( x ) sin( x ) dx (k) R sin( x ) 1+cos 2 ( x ) dx (f) R (ln( x )) 2 x dx (l) R 1 1+ e - x dx 1
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3. Find the equation of the function f ( x ) whose graph contains the point (0 , 0) and whose deriva- tive is x 3 (1 - x 4 ) 5 . 4. Suppose that the rate of change of y ( t ) is 7 t t 2 + 1 for each t . Suppose that y (0) = 1 . Find y ( t ) . 5. The half-life of radium-226 is 1590 years
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pexam1 - Math 16B: Practice problems for Midterm 1 Note:...

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