# MATH 34 Texas University Business Calculus Questions

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Math 34 Practice Exam #1
Due on date of Exam #1
Name___________________________________ Section: _________________
specified. Each question is worth 1 point and is graded on accuracy, effort, and neatness. Please show all work directly in the booklet.
**FOR INSTRUCTOR USE ONLY – DO NOT WRITE IN THE BOXED AREAS**
Neatness: __________/10
Completeness: ________/40
Problem#______: _________/25
Problem#______: _________/25
Decide whether the limit exists. If it exists, find its value.
1) Find lim f(x) and lim f(x).
x (-1)x (-1)+
Graph the function and then find the specified limit. When necessary, state that the limit does not exist.
1
2)
4×2 ,
for x -1,
f(x) = 4,
for -1 1.
Find the limit, if it exists.
x2 – 4
3) lim
x -2 x – 2
2
4) lim
x >3
x-8
Provide an appropriate response.
5) Is the function given by f(x) =
1
,
x-3
for x > 3
continuous at x = 3? Why or why not?
x2 + 5x, for x 3
Find a simplified difference quotient for the function.
6) f(x) = 2×3
Find an equation for the line tangent to the graph of the given function at the indicated point.
40
at (1, 40)
7) f(x) =
x
3
List the x-values in the graph at which the function is not differentiable.
8)
Find the derivative.
5
9) y = x4
Find all values of x (if any) where the tangent line to the graph of the function is horizontal.
10) y = x3 + 8×2 – 204x + 34
For the given function, find the points on the graph at which the tangent line has slope 1.
1
11) y = x3 – 6×2 + x
3
4
5
12) f(x) = x + (x2 – 6)
x
[Do not use algebra before differentiating]
Differentiate. Simplify. Leave the denominator in factored form.
x2 + 2x – 2
13) y =
x2 – 2x + 2
Find an expression for dy/dx.
4
and u = 7x – 5
14) y =
u2
5
Differentiate.
15) f(x) = (3 – 8x)250
Calculate the requested derivative from the given information.
16) Given f(u) = u2 and g(x) = u = x5 + 2, find (f g)'(1).
Find the indicated derivative of the function.
d3 y
x
of y =
17)
3
x
+1
dx
6
Solve the problem.
18) A company’s total cost, in millions of dollars, is given by C(t) = 220 – 60e-t where t = time in years. Find the
marginal cost when t = 4.
Differentiate.
19) y =
Solve.
4ex
2ex + 1
20) Find the equation of the line tangent to the graph of y = (x2 – x) ln (6x) at x = 2 . Approximate to the nearest
thousandth.
7
Solve the problem.
21) Suppose that P0 is invested in a savings account in which interest is compounded continuously at 5.4% per
year. That is, the balance P grows at the rate given by
dP
= 0.054P. Suppose that \$6000 is invested. What is the
dt
balance after 3 years?
22) Find the tripling time for an amount invested at a growth rate 7% per year compounded continuously.
23) An artifact is discovered at a certain site. If it has 56% of the carbon-14 it originally contained, what is the
approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.)
8
24) Find the present value of \$26,000 due 17 years later at 6.5%, compounded continuously.
Differentiate.
25) y = 5 6x
9
Testname: PRACTICE TEST 1
1) -2; -7
ID: CWAEX2B 1.1.1-1
Objective: (1.1) Find Limit Using Graph
2)
lim f(x) = 4
x -1 –
ID: CWAEX2B 1.1.3-8+
Objective: (1.1) Graph Function and Find Limit
3) 0
ID: CWAEX2B 1.2.1-7+
Objective: (1.2) Use Rational Function Limit Theorem
4) Does not exist
ID: CWAEX2B 1.2.3-3
Objective: (1.2) Find Limit of Radical Expression
5) No, lim f(x) does not exist
x 3
ID: CWAEX2B 1.2.8-8
Objective: (1.2) Determine Continuity at Point Given Function
6) 6×2 + 6xh + 2h 2
ID: CWAEX2B 1.3.1-3+
Objective: (1.3) Find Simplified Difference Quotient
7) y = – 40x + 80
ID: CWAEX2B 1.4.3-4
Objective: (1.4) Find Equation of Tangent Line
8) x = 2
ID: CWAEX2B 1.4.4-6
Objective: (1.4) Determine Differentiability from Graph
9)
dy
=
dx
5
4
5
x
ID: CWAEX2B 1.5.2-3+
Objective: (1.5) Find Derivative Using Power/Sum/Diff Rules II
10) –
34
,6
3
ID: CWAEX2B 1.5.5-8+
Objective: (1.5) Use Function to Find Points with Horizontal Tangent
10
Testname: PRACTICE TEST 1
11) (0, 0) and (12, -276)
ID: CWAEX2B 1.5.6-6
Objective: (1.5) Find Points at Which Tangent Has Given Slope
12) f'(x) = 2x x +
5
5
(x2 – 6)
+ 1x
x2
ID: CWAEX2B 1.6.2-5+
Objective: (1.6) Find Derivative of Product II
13)
dy
-4×2 + 8x
=
dx (x2 – 2x + 2)2
ID: CWAEX2B 1.6.4-2+
Objective: (1.6) Find Derivative of Quotient II
14) –
56
(7x – 5)3
ID: CWAEX2B 1.7.4-2+
Objective: (1.7) Find dy/dx Given y = f(u) and u = g(x)
15) f'(x) = -2000(3 – 8x)249
ID: CWAEX2B 1.7.1-3+
Objective: (1.7) Differentiate Using Extended Power Rule I
16) 30
ID: CWAEX2B 1.7.8-1+
Objective: (1.7) Find Derivative at Point Using Chain Rule
17) 6(x + 1)-4
ID: CWAEX2B 1.8.2-6+
Objective: (1.8) Find Higher-Order Derivative
18) 1.1 million dollars per year
ID: CWAEX2B 2.1.8-2+
Objective: (2.1) Solve Apps: Exponential and Logarithmic Functions of the Natural Base, e
19)
4ex
(2ex + 1)2
ID: CWAEX2B 2.2.2-4+
Objective: (2.2) Differentiate Exponential Function II
20) y = 8.455x – 11.94
ID: CWAEX2B 2.3.2-1+
Objective: (2.3) Find Eqn of Line Tangent To Graph at Given Point
21) \$7055.16
ID: CWAEX2B 2.4.2-6+
Objective: (2.4) Solve Apps: Business (Exponential Model)
22) 15.7 years
ID: CWAEX2B 2.4.3-5+
Objective: (2.4) Solve Apps: Effective Annual Yield, Doubling Time
23) 4639 years
ID: CWAEX2B 2.5.1-8
Objective: (2.5) Solve Apps: Radioactive Decay
24) \$8611.48
ID: CWAEX2B 2.5.3-2+
11
Testname: PRACTICE TEST 1
25) 6 · (ln 5) · 5 6x
ID: CWAEX2B 2.6.1-3
Objective: (2.6) Differentiate General Exponential Function
12