Upload
preston-lee
View
218
Download
0
Embed Size (px)
Citation preview
7/25/2019 Bc12 Fall Final Mc
1/14
BC 11-12
Fall Final Part I
No Calculator Allowed
1. An equation of the line tangent to the curve y =kx + 8
k+x atx=
!2 is y = x + 4
What is the value of k?
a) -3 b) -1 c) 1 d) 3 e) 4
2. Let f x( )be a continuous and differentiable function on the interval
0 < x
7/25/2019 Bc12 Fall Final Mc
2/14
4. The graph of a twice differentiable function f is shown below. Which of
the following is true?
(a)
(b)
(c)
(d)
(e)
5. If sin xy( ) = x2 , then dydx
=
(a) 2xsec xy( )
(b)
sec xy( )x
2
(c) 2xsec xy( )!y
(d)
2xsec xy( )y
(e)
2xsec xy( )!yx
7!
#
7/25/2019 Bc12 Fall Final Mc
3/14
6. The given functionfhas a removable discontinuity atx= -5. FindA.
f x( ) =
5x2 + 8, if x < !5
8x,
if
x =!5Ax + 8, if !5
7/25/2019 Bc12 Fall Final Mc
4/14
8. This problem involves finding the absolute maximum and absolute
minimum of the function f x( ) =x 3 ! 3x + 4 restricted to the closed interval
x! 0,
2"# $% . Which of the following statements is correct?
(a)
f x( ) has both an absolute maximum and absolute minimum at the end
points.
(b) f x( ) has both an absolute maximum and absolute minimum at interior
points.
(c) f x( ) has both an absolute maximum at an end point and an absolute
minimum at an interior point.
(d)
f x( ) has both an absolute maximum at an interior point and an absolute
minimum at an end point.
(e)
None of the above
9. Which of the following improper integrals converge?
I.
e!x
0
"
# dx II.1
x2
0
1!
"# dx III.
1
x0
1!
"# dx
(a) I only (b) III only (c) I and II only
(d) II and III only (e) I and III only
10. If f and gare continuously differentiable functions defined for all real
numbers, which of the following integrals would equal f g 4( )( )! f g 2( )( ) ?
a) f ' g x( )( )dx2
4
! b) f g x( )( )f' x( )dx24
! c) f g ' x( )( )g ' x( )dx24
!
d) f g x( )( )g ' x( )dx2
4
! e) f' g x( )( )g ' x( )dx24
!
7/25/2019 Bc12 Fall Final Mc
5/14
11. A particle is moving upward along the y-axis until it reaches the origin and
then it moves downward such that v t( ) =8 ! 2t for t! 0 . The position of the
particle at time t is given by
(a) y t( ) =!t2
+ 8t!16 (b) y t( ) =!t
2
+ 8t+16 (c) y t( ) =2t2 ! 8t!16 (d) y t( ) =8t! t2
(e) y t( ) =8t! 2t2
12.1
2
!"#
$%&
n=1
'
(2n
(a) 13
(b) 12
(c) 1 (d) 2 (e) !
13. limx!2
x2 " 4
cos #t( )dt2
x
$=
(a) 0 (b) 1 (c) 2 (d) 4 (e) DNE
14.x!x3
x2
dx1
e2
"
(a) 3! e2 (b) 3! e4 (c) 5! e2
(d) 5! e4 (e) DNE
7/25/2019 Bc12 Fall Final Mc
6/14
15. At which x-value isf(graphed above) continuous but not differentiable?
(a) 0 (b) 1 (c) 2 (d) 5 (e) nowhere
16. 6. The graph off, the derivative off,
is shown to the right. Which of the following
statements about the function are true?
I.
f is increasing on the interval !2,!1( ) .
II.
f has a minimum at x=1.
III. f is increasing on the interval !1,1( )
IV. fhas a minimum at x=!1.
(a) I and II (b) II and III (c) III and IV
(d) I and IV (e) I, II, and IV
f
7/25/2019 Bc12 Fall Final Mc
7/14
17. Iff andg are twice differentiable and if h(x) =g (f(x)), then h(x) =
(a)
g" f x( )( )
(b)
g" f x( )( )f" x( )
(c)
g" f x( )( ) f' x( )!" #$2
(d) g' f x( )( ) f' x( )!" #$2
+ f' x( )g" f x( )( )
(e)
g' f x( )( )f'' x( )+ f' x( )!" #$2
g" f x( )( )
18 The graph of f ' x( ) , the derivative of f , is shown below for !2 " x" 5 . On
what intervals is f increasing?
a) !2,1( ) only b) !2,1( ) and 1 !2,3( ) c) 3,5( )
d) 0,
1.5( )and 3,5( ) e) !2,!1( ) , 1,2( ) , and 4,5( )
7/25/2019 Bc12 Fall Final Mc
8/14
19. Which of the following differential equations corresponds to the slope field
shown in the figure below?
a)dy
dx =!
y
x b)
dy
dx =
1
5xy c)
dy
dx =
1
10xy
d)dy
dx =
y
x e)
dy
dx =
x
y
20. If f' x( ) =!4 x ! 6( )2
x ! 9( ) which of the following is true abouty=f(x)?
a) fhas a point of inflection atx= 6 and a local minimum atx= 9.
b) fhas a local maximum atx= 5 and a local minimum atx= 9.
c) fhas a local minimum atx= 6 and a local maximum atx= 9.
d) fhas a local minimum atx= 6 and a point of inflection atx= 9.
e) fhas a point of inflection atx= 6 and a local maximum atx= 9.
7/25/2019 Bc12 Fall Final Mc
9/14
BC 11-12
Fall Final Part II
Calculator Allowed
1.
2.
7/25/2019 Bc12 Fall Final Mc
10/14
3. The graph of the derivative offis shown below. Which of the following
must be true?
a) fhas a local minimum atx= -3.
b) fhas a local maximum atx= 0.
c) fis concave down on [0, 6].
d) fhas a point of inflection atx= 6.
e) fis increasing on [-3, 3].
4. At what point on the graph of f below is f' > 0
, and f" > 0
a) M b) N c) P d) Q e) R
7/25/2019 Bc12 Fall Final Mc
11/14
5.
6. If f x( ) = x2 !1 , which of the following is equal to f' 3( ) ?
(a) limx!3
x + h( )2
"1" 8
x " 3 (b) lim
h!0
x + h( )2
"1" x2"1
h
(c) limh!0
x + h( )2
"1" 8
h (d) lim
x!3
x2"1" 8
x " 3
(e) limh!0
x2"1" 8
x " 3
7. u!5
4 du1
"
#
(a) 4 (b)5
4 (c)
1
4 (d) -4 (e) DNE
7/25/2019 Bc12 Fall Final Mc
12/14
8.
9. At what point on the graph of y =1
2x2 is the tangent parallel to the line
2x ! 4y = 3
(a)1
2,! 1
2
"#$
%&'
(b)1
2,1
8
!"#
$%&
(c)1
2,!1
4
"#$
%&'
(d) 1,! 12
"#$
%&'
(e) 2,2( )
7/25/2019 Bc12 Fall Final Mc
13/14
10.
11.
7/25/2019 Bc12 Fall Final Mc
14/14
12. A particle moves along a straight line such that its position is given by
s = 4t3! 9t
2+ 6t+ 2 for t! 0 . When is the particle at rest?
(a) t=1
2 (b) t=1 (c) t= 0
(d) t= 0,1
2 (e) t=
1
2, 1