Sample Final Exam Questions
1. Differentiate with respect to x. Write your answers showing the use of the appropriate techniques. Do not simplify. √
(a) x1066 + x1/2 − x−2 ,
(b) e
x
,
(c)
sin(x) . 5 + x2
2. Differentiate, writing your answers as in problem 1. 3x
(a) e
2
cos(5x),
(b) ln(x + x + 1),
1 . (c) tan x
3. Differentiate, writing your answers as in problem 1. (a) x2005 + x2/3 ,
(b) cos(πx),
(c)
1 + 2x . 3 + x2
4. Differentiate, writing your answers as in problem 1. (a) x2 e−3x ,
(b) arctan(x),
(c) ln(cos(x)).
5. Use implicit differentiation to find the slope of the line tangent to the curve x2 + xy + y 2 = 7 at the point (2, 1).
6. 1.
2. x(x + 2) lim x→2 2x − 1
3. |4x + 4| lim + x→−1 x+1
9−t √ t→3 3 − t
lim