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Math 1205 Common Final Exam Fall 2002
FORM A
Name: ______________________________ Pledge: ______________________________ CRN: ______________________________
Instructions: Please enter your NAME, ID NUMBER, FORM DESIGNATION, and, your CRN on the op-scan sheet. The CRN should be written in the box labeled ‘COURSE’. Darken the appropriate circles below your ID number and below the Form designation letter. Use a number 2 pencil. Machine grading may ignore faintly marked circles.
Mark your answers to the test questions in rows 1 through 17 of the op-can sheet. Your score on this test will be the number of correct answers. You have one hour to complete this portion of the exam.
- The statement that (^) lim x → a
f ( x ) = 1 is FALSE for which of the following?
- (^) a = 2 and (^) f ( x ) =
x^3 − 2 x^2 x^2 − 4
- (^) a = 0 and (^) f ( x ) =
x x
- a = 0 and f ( x ) =
sin x x
- a = 0 and f ( x ) =
cos x x + 1
- Let (^) h ( x ) =
x if x < 0 1 if x = 0 x^2 if 0 < x ≤ 2 8 − x if x > 2
. Which of the following is FALSE?
- lim x → 0
h ( x ) does not exist. 2) lim x→ 2
h ( x ) does not exist.
- h has a removable discontinuity at (^) x = 0. 4) (^) lim x → 2 −^ h ( x )^ =^4
.
- lim x → 2 +^
h ( x ) = 6.
- Which of the following is FALSE?
- lim x → − 2
x ( x + 2)^2
- lim x → 1 −
1 − 2 x x − 1
= ∞ and lim x → 1 +
1 − 2 x x − 1
- f ( x ) =
2 x^2 + 3 x + 4 (2 x + 1)^2
has horizontal asymptote y =
- (^) x = 1 is a vertical asymptote for (^) f ( x ) =
x^2 + x − 2 x − 1
.
- Below is a table of values for f (1+ h ) and
f (1+ h ) − f ( 1 ) h
for h ranging from -.1 to .1.
h f (1+ h )
f (1+ h ) − f ( 1 ) h
h f (1+ h )
f (1+ h ) − f ( 1 ) h
-0.1000 3.4300 5.7000 0.1000 4.6300 6. -0.0100 3.9403 5.9700 0.0100 4.0603 6. -0.0010 3.9940 5.9970 0.0010 4.0060 6. -0.0001 3.9994 5.9997 0.0001 4.0006 6.
Which of the following statements is NOT supported by the data?
(^) lim x → 0 f^^ ′( x )^ ≈^6
(^) lim x → 1^ f^ ( x )^ ≈^4
(^) f ′( 1 ) ≈ 6
The secant line through the points (1, f (1)) and (.9, f (.9)) has slope 5.7.
The tangent line at the point (1, f (1)) has slope approximately 6.
- Following is a table of values for f , g , f ′and g ′. x (^) f ( x ) g ( x ) f ′( x ) g ′ ( x )
1 2 4 -1 3 4 -1 -2 5 2
Which of the following is FALSE?
If h ( x ) = f ( g ( x )) then h ′ ( 1 ) = 5.
If k ( x ) = f ( x ) g ( x ) then k ′( 1 ) = 2.
If (^) m ( x ) = x f ( x ) then (^) m ′ (4) = 19.
If (^) n ( x ) =
f ( x ) g ( x )
then (^) n ′ ( 1 ) =
- Which of the following is FALSE?
- If f ( x ) = x^2 +
x^2
- e + sin then f ′( 1 ) = e − 1.
If g ( x ) = sin x cos x then g ′ ( x ) = cos^2 x − sin^2 x.
If (^) h ( x ) = 17 − x^3 then (^) h ′ ( 1 ) =
.
- If k (x) = esin2x^ then k ′(0) = 2.
- If the function (^) y = f ( x ) is defined implicitly by the equation (^) y^2 + 2 x^2 y^3 + sin x = 5
then
dy dx
equals
- (^2) y + 4 xy^3 + 6 x^2 y^2 + cos x 2)
− 4 xy^3 − cos x 2 y + 6 x^2 y^2
− cos x 2 y + 12 xy^2
− 4 xy^3 − 6 x^2 y^2 − cos x 2 y
- If f ( x ) = 3 x 4 / 3− 12 x 1/3^ then f ′( x ) =
4( x − 1) x 2 / 3^
. On the interval [-1,8] which of the
following is FALSE?
- The critical numbers for f are (^) x = 0 and (^) x = 1.
- f has neither a local maximum nor a local minimum at (^) x = 0.
- f has a local minimum at x = 1.
- The absolute maximum value for f is 15.
- The absolute minimum value for f is (^) − 9.
- If y = sin( x^2 ) and the value of x increases from 1 to 1.01 then using differentials to approximate the corresponding change in y gives
- (^) −.02 2) (^) .02 3) 0 4) .01 5) (^) −.
- The figure below gives the graph of the derivative, (^) f ′( x ), for a function (^) y = f ( x ).
Graph of (^) f ′( x )
Which of the following is TRUE about the function f ( x )?
- (^) f is increasing on the interval (a,c).
- f has a local maximum at x = c and a local minimum at x = e.
- f has a local maximum at x = d and local minima at x = b and x = f.
- (^) f is concave up on the interval (d,f).
- (^) f is concave up on the interval (c,e).
- A landowner wishes to create a 1200 ft^2 rectangular field adjacent to an existing wall. The field is to be divided into two equal parts as shown below. No fencing is required along the wall. What is the minimal length of fencing required to enclose the field? y y
x x x
(existing wall)
- 50 ft 2) 120 ft 3) 60 3 4) 20 ft 5) 30 ft
(^0) a b c d e f g
