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Calculus 1 st^ Common Assessment Review Name________________
Use the graph at the right for problems 1 and 2.
1. Find lim x → 1 f ( x )
[A] DNE [B] − 2 [C] − 5 [D] ∞ [E] 0
- Find lim x → 7 f ( ) x
[A] DNE [B] 5 [C] 2 [D] ∞ [E] 0
- Evaluate lim 7 3 2 x 7
x → x
[A] − 4 [B] 1
− [C] DNE [D] 1
[E] 4
- Evaluate (^7) 6
lim tan x π x →
[A] 1
[B] 3 [C] 3
[D] 3
[E] 2
- Evaluate (^5)
lim x 5
x →+ x
[A] − 2 [B] 1 [C] − 1 [D] DNE [E] 2
- Evaluate
2 1 lim 2 1 x 2 4 1
x x →− x x
[A] 3 [B] − 6 [C] DNE [D] 1 [E] 0
- Evaluate
2 3 2 lim^6 11 x 5 12 9
x x →− x x
[A] 25
− [B] 25
− [C] 0 [D] 11
[E] 25
- Evaluate 3 4
lim sec 2 x π + x →
[A] 0 [B] ∞ [C] −∞ [D] DNE [E] 1
- Evaluate lim 3 2 3 x 6 9
x →−− x x
[A] ∞ [B] 0 [C] DNE [D] −∞ [E] − 6
- Evaluate (^1)
lim 3 2 1 x 1
x → x
[A] 4
− [B] 4
[C] DNE [D] 9 [E] 4
- Find all of the non-removeable discontinuities for
2 2
f x x^ x x x
= −^ −
[A] (^) x = 1, − 4 [B] (^) x = 4, − 1 [C] (^) x = 1 [D] (^) x = − 4 [E] None
- Evaluate
2 0 lim 2 7 5 x 1
x x → x
[A] 5 [B] 0 [C] DNE [D] − 5 [E] 12
- Evaluate lim 2 3 5 x 2
x → x
[A] 0 [B] DNE [C] 2 5 [D] 1
[E] 5
20. The 0 (^ )
sin 2 sin 2 lim →
h
x h x h
is
[A] nonexistent [B] −2 cos 2 x [C] 2 cos 2 x [D] − cos 2 x [E] 0
- The
0
lim →
h
x h x h
is
[A] nonexistent [B] − 2 x [C] 0 [D] 2 x + h [E] 2x
22. An equation of the line tangent to the graph of f ( ) x = 2 x ( 1 − 3 x )^2 at the point (1, 2 ) is
[A] y = 32 x − 30 [B] y = 2 [C] y = 32 x − 34
[D] y = 24 x − 22 [E] y = 24 x − 26
23. If ( )
2 2
f x x^ x x x
, then f ′^ ( x )=is
[A] 1 [B]
2 2
x x
[C]
( )^2
x −
[D]
2 2
x x x
[E]
3 2 2
x x x x
24. If f ( x ) = sin x +cot x , then f ′ ( x )=
[A] cos x −tan x [B] − cos x +csc^2 x [C] cos x −csc^2 x
[D] cos x +csc x cot x [E] − cos − csc x cot x
25. If f ( x ) =cos^2 x , then f ′′^ ( π)=
[A] − 2 [B] 0 [C] 1 [D] 2 [E] 2 π
26. If f ( x ) = x^2^ cos 2 , x find f ′( x ).
[A] 2 x sin 2 x [B] (^) − 2 x cos 2 x + 2 x^2 sin 2 x [C] − 4 x sin 2 x
[D] 2 x cos 2 x − 2 x^2 sin 2 x [E] 2 x −2sin 2 x
- An equation of the line tangent to y = 4 x^3^ − 7 x^2 at x = 3 is
[A] y + 45 = 66 ( x + 3 ) [B] 45 1 ( 3 )
y − = − x − [C] y = 66 x
[D] y = 66 ( x − 3 ) [E] y − 45 = 66 ( x − 3 )
- What is the equation of the line tangent to the graph of (^) y =sin^2 x at? 4
x =^ π
[A] 1
− = − ^ −^ π
y (^) x (^) [B]
− = ^ −^ π
y (^) x (^) [C]
− = ^ −^ π
y (^) x
[D] 1 1
− = ^ −^ π
y (^) x (^) [E]
− = ^ −^ π
y (^) x
29. Determine the point(s) (if any) at which f ( x ) = 3 x^3^ + 9 x^2 has a horizontal tangent line.
[A] ( −2, 0 , 0, 0 ) ( ) [B] ( −2,50 , 0, 0 ) ( ) [C] ( −2,12)
[D] ( −2,12 , 0, 0 ) ( ) [E] none
30. Determine the point(s) (if any) at which ( )
2 2 3
f x x x
has a horizontal tangent line.
[A] ( 0, 0 ,) ( −3, − 3 ) [B] ( 0, 0 ,) ( −3, 0 ) [C] ( −3, − 3 )
[D] ( 0, 0 , 3,1) ( ) [E] none
37. Find the equation of the tangent line to the function y = 4 x ( 1 − x )^3 at ( 2, − 3 ).
- Find^ d^^5 62 3 x^3 dx x x
- Evaluate lim x → 6 2 x − 10
- Evaluate (^3)
lim →−+ 3
x +
x x
- Evaluate (^3)
lim 1 →− 3
x +
x x x
Find f ′^ ( x ) for each of the following.
42. f ( x ) = sec 2 x − cos 3 x +csc x
43. f ( x ) = x^3^4 x + 3
2 2
f x x x
45. f ( x ) =cot x^2
46. f ( x ) = tan 4( x^2 + 3 x )
