Math 1100 Section 4 Review 1 (1.4-2.5) Due: Day of Test 1
This will be graded on completion so try all of the problems. And unless otherwise
stated do not simplify your answer!!
p
1. If f (x) = x + x and g(x) = 2x + 5 nd
3
2
(a) f(2)
(b) g(-2)
(c) f(g(f(x)))
(d) g(f(-1))
x 1
2. Find xlim
! x 1
2
1
3. Find lim
s!
5
s
2
0
4. Find ylim
(y
!
2
4
+s
s
5
+2
6y + 10)
5. Say H (x) = x2x2 x . On what intervals is H (x) continuous? If
H(x) has any discontinuities determine where they are and of what
type they are.
0
6. Determine wheather or not the function G(x) = x x++35 xx <0
is continuous on R
7. Using the limit de nition of the derivative nd f 0(x) when f (x) =
4x x + 6
8. Using the limit de nition of the derivative nd g0(x) when g(x) =
+3 +2
1
2
2
1
2x+1
9. If f (x) = x x nd f 0(1)
p
10. If g(x) = x2 + x nd the slope of the tangent line at (1; 2)
11. Find dxd [x 3x 10]
12. If T (x) = x2x then nd the equation for the tangent line at the
point (2; )
3
13
1
5
2
3
11
2
1
13. Say that your car is moving down a highway with the distance (in
miles) it has traveled after t hours given by the function P (t) =
x + 6x + 9. Find the speed of the car when t = 4 hours.
14. Find the marginal cost for producing x units when the cost function is C (x) = 25x 10x .
15. Find the marginal revenue for producing x units when the revenue
funtion is given by R(x) = 240x 30x
16. Given the above cost and Revenue functions nd the marginal
pro t for producing x units.
p
17. If f (x) = ( x + x )( x + x) nd f 0(x).
18. If f (x) = x2 x x then nd f 0(x).
19. If A(x) = p x then nd A0(x).
3
4
2
5
2
6
1
3 +2
8 +5
10
3 +1
20. If B (y) =
2y 2
(y +3)3
p
then nd B 0(y).
1. If T (x) = p5x3x x then nd T 0(x).
2. Use the limit de nition of the derivative to nd Q0(x) where Q(x) =
px .
3. Give an example of a di erentiable function that is continuous on
the whole real line with non-constant derivative. And a function
that is continuous everywhere except 0 and 6 and whose range is
[0; 1) and wherever its derivative is de ned it is not constant
4. Timmy's dad is driving down the road with a distance given by
the function D(t) = at + bt + 10 where a; b 2 R. If his velocity at
t = 6 is 24mph and at t = 9 it is -4mph (driving back home). Then
at what time did he turn around? (Hint nd when the velocity is
equal to zero.)
5
2 +5
5 +1+2
5
4 +5
2