Homework Seven Sections 2.4 and 2.5 Bittinger-Ellenbogen: Calculusand its Applications
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1)
1)
For the graph of f(x) above,
i) Determin
Homework Six Sections 2.1 and 2.2 Bittinger-Ellenbogen: Calculusand its Applications
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Determine where the function f graphed below
Formula Sheet:
limit of (sin(x)/x) as x approaches 0
1
limit of (1-cos(x)/x) as x approaches 0
0
Derivative of sin(x)
cos(x)
Derivative of cos(x)
-sin(x)
Derivative of tan(x)
sec^2(x)
Derivative of csc(x)
-csc(x)cot(x)
Derivative of sec(x)
sec(x)tan(x)
De
Theorem Notes:
Intermediate Value Theorem
-if f is continuous for all x in interval [a, b] and y is a number between f(a) and f(b), then there's a
number x=c in (a, b) for which f(c)=y
-basically, if you have a continuous function and you pick a number on
Functions , graphs and limits notes:
derivative at a point
the slope of the tangent line at a specific point on the graph of a function
definite integral
the area of the region in the coordinate plane bounded by a function and the x-axis, with upper and
l
Derivative Rules and Techniques:
If f(x) = c then f'(x) = _
f'(x) = 0
?
If f(x) = x? then f'(x) = _
f'(x) = nx?
?
If f(x) = c ?x? then f'(x) = _
f'(x) = c ?nx?
?
If f(x) = u(x) v(x) then f'(x) = _
f'(x) = u'(x) v'(x)
- The derivative of a sum (difference)
Review 2:
What is the definition of the derivative?
f'(x) = lim (x0) [( f(x + x) - f(x) ) / (x) ]
What are two ways to find f'(c) using the definition of the derivative and the
alternate form of the definition of the derivative?
f'(c) = lim (x0) [( f(c +
Quiz 1 review:
slope-intercept form
y = mx+b
slope
rise/run
point-slope form
y - y1 = m(x - x1)
general form
Ax + By = C
parallel
same slope
perpendicular
slopes that are opposite reciprocals
increments
the change in x or y
increment
1st value - 2nd value
Review 1:
The existence or nonexistence of f(x) at x=c has no bearing on the existence of
what?
The limit of f(x) as x approaches e
What are the three common types of behavior associated with the nonexistence of a
limit?
1. f(x) approaches a different num
Homework Five Sections 1.7 and 1.8 Bittinger-Ellenbogen: Calculusand its Applications
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Determine the derivative of f(x) = (4x + 3)5