PRACTICE PROBLEMS

# PRACTICE PROBLEMS - x 9(c f x = e sin x(d h x = ˆ x 2-ln x...

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Review Problems for exam 1 Note: these problems are in addition to the homework problems. You can watch the solutions on the posted streaming power points. 1. Let F ( x ) = x 3 + A x 2 6 x + 1 2 < x < 3 x 2 + 2 x 3 (a) Find the value of A that makes F ( x ) continuous at x = 2. (b) For the constant A from (a): is F ( x ) diﬀerentiable at x = 2? (c) Is F ( x ) diﬀerentiable at x = 3? 2. Show that the equation x 3 = x 2 + 1 has at least one solution. 3. Use the deﬁnition of the derivative as a limit to ﬁnd the derivative of f ( x ) = 1 x + 2 4. Find the center and the radius of the circle x 2 + y 2 - 2 x + 4 y = 0 5. Evaluate each of the following limits. (a) lim x 3 x - 3 x - 3 + 3 x 2 (b) lim x 0 tan (5 x ) sin(3 x ) (c) lim x 3 | x - 3 | x 2 - 9 6. Find the derivatives of the following functions. (a) F ( x ) = s e x x 2 + 3 (b) g ( x ) = 3cos 4 x · sin
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Unformatted text preview: x 9 (c) f ( x ) = e sin x (d) h ( x ) = ˆ x 2-ln x 3 x + 2 ! 9 (e) F ( x ) = tan x ( x 2-4 x ) ln x 7. Let g ( x ) be a diﬀerentiable function such that g (1) = 2 , g (2) = 5 , g (3) = 7 , g (4) = 2 , g (1) = 3 , g (2) = 2 , g (3) = 8 , g (4) = 10. Let f ( x ) = x 2 + x . Find the exact value of: (a) ( gf ) (2) (b) ˆ f g ! (3) (c) ( g ◦ f )(1). 8. Solve log (5 x ) + log ( x-1)-2 = 0 9. (a) Describe the rectilinear motion given at time t (in seconds) by s ( t ) = 20 + 8 t-t 2 (in meters), for 0 ≤ t ≤ 10. (b) Find the total distance traveled. 10. Find the domain of the function f ( x ) = ln( x 2-4) 1...
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## This document was uploaded on 11/02/2011 for the course MATH 135 at Rutgers.

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