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Unformatted text preview: Additional 151 review problems for final exam Note: the material covered in this set of problems doesn't contain the material that is common to Calculus 135 and 151. It is useful for 151 students only. 1. Evaluate lim n 2k(k + 1) n3 k=1 n 2. Find the area of the region that is enclosed between the curves y = 2x and y = x2 - 3. 1 3. Show that the derivative of the function f (x) = tan-1 x is using the fact that 1 + x2 y = tan-1 x if"f tan y = x and - < x < . 2 2 4. Differentiate f (x) = tan-1 (ex ). 2 5. Find: (a) (b) ex dx 1 + e2x e2x dx 1 + e2x 6. Evaluate 3 0 9 - x2 dx 7. Find lim +
x0 x 0 sin (t2 )dt . x3 1 ...
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