AMAT 217 Final - Fall 2010
-
Upload
stacy-smith -
Category
Documents
-
view
214 -
download
0
Transcript of AMAT 217 Final - Fall 2010
-
8/13/2019 AMAT 217 Final - Fall 2010
1/16
University of Calgary - Faculty of Science
Department of Mathematics and Statistics
AMAT 217-L01 - L06 - Fall 2010 - Final Examination
Closed Book , No Calculators.
01.Let g ( x) =ax 2 + b x 2
8 x 3 x > 2
Find the values of the constant real numbers a and b such that the function g is differentiable at x = 2.
02. Find an equation of the line tangent to the curve y = x3 x 1 which passes through the point (0 , 3).
03. Determine the slope of the line tangent to the curve sin ( y 1) = x3 + xy2 2 at the point (1, 1 ) on the curve.
04.Evaluate 24 x4 + x2 + 3 x2 dx
05. Assume the function f ( x) = x2 2 x + 3 , x 1 has an inverse. Find a formula for y = f 1 ( x)
06.Let g be an inverse function of f . Using the table of values below, find g ( 12
).
x f ( x) f ( x)
2 4 5
9 12
7
07.If y = cos(e x) + e cos ( x) , find dy
dx
.
08. Find the derivative of y = [cosh ( x)] x.
09. The half life of a radioactive substance is 60 years. In how many years will three fourth of the original
amount have disintegrated?
10.If sinh ( x) = 43
, find the exact value of cosh ( x).
11.The voltage V in volts , the resistance R in ohms , and the current I in amperes are related by the
formula V = I R . The current in an electrical system is decreasing at the rate of 3 amperes / s while
the voltage remains constant at 9 volts .
At what rate is the resistance changing at the instant the current is 6 amperes ?
12. Newtons method with initial approximation x0 is used to approximate a real root of the equation
x4 2 = 0. Determine the value of Newtons method iteration x1 .
13.Evaluate x 2lim 2 x
3 3 x2 12 x + 24 x3 x2 8 x + 2
-
8/13/2019 AMAT 217 Final - Fall 2010
2/16
14.Find x 2+lim (5 x2 )
1 x2
15.Let f ( x) = 3 x4 4 x3 + 5 . Find the x and y coordinates of local maxima & local minima of the function f .
16.Let f ( x) = 18( x 2) 2/3 + 9( x 2) 1/3 .The first and second order derivatives of f are respectively given by
f
( x) = 3(4 x 9)
( x 2) 4/3 , f
( x) = 4(3 x)( x 2) 7/3 . Determine the x and y coordinates of points of inflection of f .
17. Find the equations of the vertical asymptotes of
f ( x) = x2 + x + 2 2 x4 x2
.
18. Find the equations of the horizontal asymptotes of the function
f ( x) =
12 x2 x2 + 2
x < 4
5 + 6 e x
1 + 2 e x x 4
19. Find the the linearization L( x) of f ( x) = tan 1( x) about x = 1.
20.Let L( x) be the linearization of the function f about x = a. Assume that f is concave up
on an open interval containing a. Which of the following statements is true :
(I) f ( x) > L( x) for all x near a. (II) f (a ) > L(a )
(III) f ( x) < L( x) for all x near a. (IV) f (a ) < L(a )
21.Evaluate 6 x(6 x 1) 2 dx .
22.Find 1e x + e x dx
23.Determine x 0lim
02 x
(e t 2
1) dt
x3
24. Find the area of the region enclosed by the parabola y = 3 x2 x and the straight line y = 5 x.
25. Calculate the volume of the solid generated by revolving the region between the curves
y = x2 , y = 3 x , 0 x 1 , about the y axis.
-
8/13/2019 AMAT 217 Final - Fall 2010
3/16
-
8/13/2019 AMAT 217 Final - Fall 2010
4/16
-
8/13/2019 AMAT 217 Final - Fall 2010
5/16
-
8/13/2019 AMAT 217 Final - Fall 2010
6/16
-
8/13/2019 AMAT 217 Final - Fall 2010
7/16
-
8/13/2019 AMAT 217 Final - Fall 2010
8/16
-
8/13/2019 AMAT 217 Final - Fall 2010
9/16
-
8/13/2019 AMAT 217 Final - Fall 2010
10/16
-
8/13/2019 AMAT 217 Final - Fall 2010
11/16
-
8/13/2019 AMAT 217 Final - Fall 2010
12/16
-
8/13/2019 AMAT 217 Final - Fall 2010
13/16
-
8/13/2019 AMAT 217 Final - Fall 2010
14/16
-
8/13/2019 AMAT 217 Final - Fall 2010
15/16
-
8/13/2019 AMAT 217 Final - Fall 2010
16/16