BUSINESS CALCULUS EXAM
QUESTIONS AND ANSWERS
Find the limits of the following three functions:
A. Lim 4x-3/2x+1 as x -->∞
B. Lim 3x/4x^2-1 as x -->∞
C. Lim 5x^2/x+3 as x -->∞ - ANSWER-B. A: 2, B: 0, C: -∞
Find the vertical and horizontal asymptotes and write them as equations of lines for the
function f(x) = 3x^2/2(x^2+1) - ANSWER-C. VA: None & HA: y= 3/2
The demand function for a product is modeled by the function p=75-0.25x where p is
the price per unit (in dollars) and x is the number of units. Use differentials to
approximate the changes in revenue as sales increase from 70 units to 71 units. -
ANSWER-B. 39.75
If a derivative of a function f(x) is a linear function, then which one of the following
functions represents f(x)? - ANSWER-B. f(x) = -4x^2 + 17 + 41x
Which one of the following is the "Second Derivative Test"? - ANSWER-A. Suppose f'(c)
=0, and let f"(x) exist on an open interval containing c.
If f"(c) > 0, then f(c) is a relative maximum.
If f"(c) < 0, then f(c) is a relative maximum.
If f"(c) = 0, then the test fails.
Find the domain of the function f(x) = x/√x-4 - ANSWER-C. Domain: (4,∞)
Find the limit of f(x) as x --> 3 where f(x) = { 1/3x-2, x≤3
-2x+5, x>3 - ANSWER-D. Limit = -1
Find the limit, as x--> 0, of f(x) - √x+1 -1/ x - ANSWER-C. Limit = 0.5
Find the interval on which the function f(x)= 2(x+5)/x^2+25 is continuous. - ANSWER-B.
(-∞,∞)
Find an equation of the line that is tangent to the graph of f(x)= -1/2x^3 and parallel to
the line 6x+y+4=0. - ANSWER-A. 6x+y-8=0 and 6x+y+8=0
Read the following three statements A, B and C.
A. The slope of the graph of f(x)= x^2 is different at every point on the graph of f.
B. If a function is continuous at a point, then it is differentiable at that point.
C. If a function is differentiable at a point, the it is continuous at that point.
QUESTIONS AND ANSWERS
Find the limits of the following three functions:
A. Lim 4x-3/2x+1 as x -->∞
B. Lim 3x/4x^2-1 as x -->∞
C. Lim 5x^2/x+3 as x -->∞ - ANSWER-B. A: 2, B: 0, C: -∞
Find the vertical and horizontal asymptotes and write them as equations of lines for the
function f(x) = 3x^2/2(x^2+1) - ANSWER-C. VA: None & HA: y= 3/2
The demand function for a product is modeled by the function p=75-0.25x where p is
the price per unit (in dollars) and x is the number of units. Use differentials to
approximate the changes in revenue as sales increase from 70 units to 71 units. -
ANSWER-B. 39.75
If a derivative of a function f(x) is a linear function, then which one of the following
functions represents f(x)? - ANSWER-B. f(x) = -4x^2 + 17 + 41x
Which one of the following is the "Second Derivative Test"? - ANSWER-A. Suppose f'(c)
=0, and let f"(x) exist on an open interval containing c.
If f"(c) > 0, then f(c) is a relative maximum.
If f"(c) < 0, then f(c) is a relative maximum.
If f"(c) = 0, then the test fails.
Find the domain of the function f(x) = x/√x-4 - ANSWER-C. Domain: (4,∞)
Find the limit of f(x) as x --> 3 where f(x) = { 1/3x-2, x≤3
-2x+5, x>3 - ANSWER-D. Limit = -1
Find the limit, as x--> 0, of f(x) - √x+1 -1/ x - ANSWER-C. Limit = 0.5
Find the interval on which the function f(x)= 2(x+5)/x^2+25 is continuous. - ANSWER-B.
(-∞,∞)
Find an equation of the line that is tangent to the graph of f(x)= -1/2x^3 and parallel to
the line 6x+y+4=0. - ANSWER-A. 6x+y-8=0 and 6x+y+8=0
Read the following three statements A, B and C.
A. The slope of the graph of f(x)= x^2 is different at every point on the graph of f.
B. If a function is continuous at a point, then it is differentiable at that point.
C. If a function is differentiable at a point, the it is continuous at that point.
