Calculus Test Chapter 4 /50
1. State the equation of the tangent line of y = ax2 c, at x = 2.
(3)
2. Using the Mean Value Theorem, write an equation for:
a) the secant line
b) the tangent line
(5)
f(x) =
1 x 3
x 1
3. Find the function with the given deriv
Calculus Quiz #2 /40
1. Using the definition of the derivative, state the derivative for y = 3x2 4x.
(3)
2. f(x) = cfw_ x2 + 3 , x < 1
cfw_ 2x + 2 , x 1
(8)
a) For the function f(x) state the following:
i) lim x 1ii) lim x 1+
iii) lim x
1
b) Calculate th
Calculus Test 1
/55
1. Find an equation perpendicular to 2x + y = 4, and through the point (-2, 2).
(2)
2. Prove that the function is even, odd, or neither: y = x + cos x
(3)
3. Graph the piecewise function and state the domain and range:
y = cfw_ 4 x2 ,
Calculus Quiz /30
1. State the derivatives of the following functions:
tan x
x
a) y = x2sinx
b) f(x) =
c) y = cos( t3 1)
d) y = sin2 (3x 3)
e) y =
3
f) Find
2x 1
g) x2 xy + y2 = 7
j) If
d
sin-1 u =
dx
h) y2 =
1
1 u
2
x 1
x 1
dy
if x = 2cost and y = 2sint
Chapters 5&6
1.a) For the function y = lnx + x2, estimate the area under the curve between x = 1 and
x = 3, using the left rectangular approximation method with 4 rectangles. Be sure to
include an appropriate diagram.
b) Repeat the previous step for RRAM.
Chapter 5 Calculus Test /50
1.a) For the function y = 4x x2, sketch the graph between 0 x 4 .
(8)
b) Partition [0,4] into 8 subintervals and show the 8 rectangles that RRAM uses to
approximate the area between the curve and the x axis.
c) Using the RRAM e
Calculus Practice Test Chapter 4
1. State the equation of the tangent line of y = ax2 c, at x = 2.
(3)
2. Using the Mean Value Theorem, write an equation for:
a) the secant line
b) the tangent line
(5)
f(x) =
1 x 3
x 1
3. Find the function with the given
Calculus Quiz Chapter 2 /40
1. f(x) = cfw_ x2 + 4 , x < 1
cfw_ 3x + 3 , x 1
(5)
a) For the function f(x), graph the function and state the following:
i) lim x 1ii) lim x 1+
iii) lim x 1
2. For the following function f(x), state:
a) lim x -1- b) lim x -1+
Calculus Assignment /50
1. The function v(t) is the velocity in m/sec of a particle moving along the x-axis.
v(t) = t3 4t2 + 3t,
0 t 5
Algebraically, determine the following:
a) When the particle is moving to the right, to the left, and stopped.
b) Find t
Calculus Test Chapter 3
/50
1. a) Using the definition of the derivative, develop the derivative for y = 37x.
(6)
b) Find the equation of the tangent line at x = 0.5.
2. Find
dP
nRT
an 2
in which a, b, n, R, T are constants: P =
+ 3
dV
2V nb
V
(4)
3. The
Integration Quiz /30
Do the following using Integration by Parts:
ln x
dx
x5
1.
2.
x2e3x dx
3.
x3ln5x dx
4. (lnx)2 dx
= 1 dx)
5.
udv uv vdu
Hint: (Integration by parts has to be done twice, both times let dv
xcos3x dx
Do the following using Integration
Chapter 6 Calculus Test /50
1. Evaluate the integral:
5
a) (et/2 - 2 ) dt
t
(4)
b)
( 3sinx sin 3x) dx
2. Solve the initial value problem:
a)
(6)
d2y
= 2 6x , y(0) = 1, y (0) = 4
dx 2
b) State the equation of an objects velocity and its displacement, if t
Calculus Test Chapter 3
/45
1. a) Using the definition of the derivative, develop the derivative for y = 2x.
(5)
b) Find the equation of the tangent line at x = 2.
2. Determine if the following function is differentiable at x = 0.
(5)
f(x) = cfw_ x2, x 0
1. Dierentiate implicitly:
(a) xy = x y 2
(b) y +
x + y3 = 1
2. A spherical balloon is being inated. If the volume is increasing at a rate of 2cm3 per
minute, at what rate is the radius changing when the radius is 10cm?
3. An 8m ladder rests against a ver
MAT 1308
Introduction to Calculus
Summer 2008
Calendar description: Review of elementary functions. Introduction to
limits. Geometric series. Introduction to dierential and integral calculus in one
variable with applications.
Linear approximations, applic
1. Dierentiate implicitly with respect to x:
(a) 2xy = x y 2
d
(2xy)
dx
dy
2y + 2x
dx
dy
dy
+ 2y
2x
dx
dx
dy
(2x 2y)
dx
dy
dx
(b) y +
=
=
d
(x y 2 )
dx
dy
1 2y
dx
=
1 2y
=
1 2y
=
1 2y
2x 2y
x + y3 = 1
The easiest way to handle this is to rewrite before di
Worksheet on Integration
1. Evaluate the following indenite integrals:
2
2x7 x4/3 + 17
x x
x+1
dx
2 + 2x 3
x
(a)
(b)
dx
x3 ln x dx
(c)
(ln x)3
dx
x
x3 x4 2 dx
(d)
(e)
(f)
x2 e5x dx
(g)
x 3 x 1 dx
2. Evaluate the following denite integrals:
e
x2 ln x dx
(a
MAT 1340 Assignment 1
Due in class, Tuesday, September 25
This assignment consists of eight questions on material from Section 1.1 to Section 1.7
(inclusive). Show all relevant workings.
1. Consider the diagram below, in which ABCD is a rectangle with sid
MAT 1340 Assignment 2
Due in class, Tuesday, October 23
Show all relevant workings.
1. Determine if the following lines intersect. If so, nd their point of intersection and
acute angle of intersection.
L1 : x = 5 + 2t
y = 1 5t
and
L2 :
x1
y+2
=
.
3
1
2. L
MAT 1340 Assignment 3
Due in class, Tuesday, November 6
Show all relevant workings.
1. Solve the following systems, if possible. Use row reduction.
(a)
3x + 2y z = 6
x 4y + z = 7
2x 6y 5z = 1
(b)
2x + 3y z = 2
x 2y + 5z = 3
4x y + 9z = 1
2. Two planes 1 a
Calculus Quiz /30
1. State the derivatives of the following functions:
tan x
4x
a) y = x2sin3x
b) f(x) =
c) y = cos( t3 t)
d) y = sec2 (3x 3)
e) y =
3
2x 1
g) x2 xy + y2 = 7
f) Find
dy
if x = 2cost and y = 2sint
dx
h) y2 =
x 1
+ 3y
x 1
i) xy + sin(xy) = 3