# SOLUTION: MATH 110 University at Albany Section 1 LHS and RHS Limit Calculus I HW

Math 110 - Calculus I
Section I- Multiple Choice
Students Name
Questions 1 and 2 relate to the diagram adown.
y
4
3
2
1
x
–3
–2
–1
1
3
2
–1
4
5
6
7
–2
–3
1.
What is the compute of
lim f (x) .
x5
B. – 1
A. Does not await
2. What is the compute of
C. 4
D. 1
E. Some other response
C. 2
D. 1
E. Some other response
lim f (x) .
x1
A. Does not await
B. – 1
x2 9
3.
What is the compute of the lim
x3
A. 6
B. 0
x 3
.
C.
D. – 3
E. Some other response
Page 1
x
4.
5.
For what compute(s) of x is the exercise f(x) =
6.
C. x = 1 and x = – 1
B. x = 1
D. x = 0 , x = 1 and x = – 1
E. Some other response
3
What is the compute of the aftercited proviso lim 4x 1
x2x 2 2
B. 0
C.
D.
B. ½
C.
D.
1
B. 0
C.
D.
2
8.
E. Some other response
3
lim 2x 1
x4x3 2
What is the compute of the aftercited proviso
A.
E. Some other response
lim 4x 1
x2x 2
What is the compute of the aftercited proviso
A. 2
7.
x 1
A. x = 0
A. 2
not normal?
2
The equation of the tangent cord to the incurvation y = 2 x
2
E. Some other response
at the summit (1,0) is:-
x
9.
A. y = 2x – 1
B. y = 2x + 1
D. y = 2
E. Some other response
C. y = 2x
The equation of the tangent cord to the incurvation y = x3 – 5x + 3 at the summit (2,1) is:A. y = 8x + 13
B. y = – 9x – 13
D. y = –7x + 13
E. Some other response
10. What is the derivative of the exercise y =
x
A.
1
2 x
D.
1
2 x
1
2 x3
1
1
2 2
B.
1
2 x
1
x
C. y = 7x – 13
2
1
2 x3
1
2 2
C.
1
2 x
1
2 x3
E. Some other response
2 x3
Page 2
11. The pose of a jot is loving by the formula s(t) =
1
cos (2 t)
(delay t 0 ).
4
What is the acceleration when t = 5
A.
B. 2
0
D. – 2
C. – 4 2
E. Some other response
12. What is the derivative of y = x2 e2x
A. 2xe2x + x2ex
B. 2xe2x + 2x2e2x
D. xe2x + 2x2e2x
E. Some other response
C. xe2x + x2e2x
t 2 1
13. What is the derivative of g(t) =
t 1
t 2 t 1
A. 1
D.
B. 2t
t 2 t 1
C.
E. Some other response
t 12
14. What is the derivative of f(x) = sin( 2x 1)
A.
cos
2x 1
B.
2x 1
2x 1
D. cos
t 12
2 cos 2x 1
2x 1
C.
cos
2x 1
2 2x 1
E. Some other response
15. For h(x) = x3 + 5x2 – e4x what is h(x) the third derivative of h(x)?
A.
6 – e4x
B. 6 + e4x
D.
6 – 64e4x
E. Some other response
C. 6
Page 3
16. The pose of a jot is loving by the formula s(t) = t3 – 1.5t2 – 2t (delay t 0 ).
What is the acceleration when t = 5
A.
27 m/sec2
C. – 27 m/sec2
B. 35 m/sec2
D. – 35 m/sec2
E. Some other response
17. The pose of a jot is loving by the formula s(t) =
1
cos (2 t)
(delay t 0 ).
4
What is the acceleration when t = 0
A.
B. 2
0
D. – 2
C. – 4 2
E. Some other response
18. Use logarithmic differentiation to lump the exercise y = x6x.
A.
dy
= x6x
B.
dx
D.
dy
dy
= 6x6x(6ln x + 1)
dx
= x6x(6ln x + 1)
C.
dy
= 6x6x(ln x + 1)
dx
E. Some other response
dx
19. For the exercise y =
x what is the equation of the cordar bearing exercise at x = 4
A. y = 2
B. y = ¼ x
C. y = ¼ x + 1
D. y = ¼ x + 2
E. Some other response
20. Experience the independent stint compute of y = x3 – 3x on the season [0,2].
A. 0
C. – 2
B. 2
D. – 3
E. Some other response
21. Experience all the exact total for f(x) = x4(x – 3)3
A. x = 0 , x = 2 and x =
C. x = 0 , x = 3 and x =
12
7
12
7
B. x = 0 , x = 3 and x =
D. x = 0 , x = 2 and x =
12
11
12
11
E. Some other response
Page 4
22. On what season is f(x) = x4 – 6x2 excavated down.
A. (– 1, 1)
B.(0,1)
C. (– 1, 0)
D. ( , 1)
E. Some other response
23. If f (1) = 0 and f (1) – 2 then which of the aftercited is a argumentative conclusion
A
There is a topical climax at x = 1
B
There is a topical stint at x = 1
C
There is a summit of inflexion at x = 1
D
There is a perpendicular asymptote at x = 1.
E. Some other response.
24. If f (x) f(x)
which one of the aftercited statements is penny.
B. f(x) = ex + cx
A. f(x) = x
D. It is unusable for a exercise to have
C. f(x) = ex + cx + d
f (x) f(x)
E. None of the statements are penny.
25. If f (x) 3x2 4x 1 and f(0) = 1 Then
A. f(x) = x3 + 2x2 + 1
B. f(x) = x3 + 2x2 + x + 1
D. f(x) = 6x + 1
E. Some other response.
C. f(x) = 6x + 4
26. If f (1) = 0 and f (1) – 2 then which of the aftercited is a argumentative conclusion
A
There is a topical climax at x = 1
B
There is a topical stint at x = 1
C
There is a summit of inflexion at x = 1
D
There is a perpendicular asymptote at x = 1.
E. Some other response.
27. Experience the independent climax compute of y =
A. 10
B. 81
C. 8
81 x 2 on the season [– 9,9].
D. 1
E. Some other response
28. Experience f(x) when f (x) = 12x + 24x2
A. f(x) = 6x3 + 4x4 + cx + d
B. f(x) = 2x3 + 2x4 + cx + d
C. f(x) = 4x3 + 8x4 + cx + d
D. f(x) = 2x3 + x4 + cx + d
E. Some other response
Page 5
Section II.
In this individuality it is sharp to parade appropriate instituted as security can barely be loving for instituted that is paraden.
You must as-well response using the regularity asked in those questions that state a point regularity.
1. Experience the aftercited provisos by algebraic resources – Do not use L’Hospitals Rule.
(a)
2
lim x 4
x2 x 2
1
lim 1h
(b) h0
h
2. By using provisos and primary principals experience f (a) for the exercise f(x) = x2 – x.
Page 6
3. Draw a portray of y = f (x) by using the graph of y = f(x).
y = f(x)
4. Lump the exercises:(a) f(x) = 2x3 +
4
+
2
x
4.(b)
h(x) =
4 e x
x2
Page 7
5.
4.(c)
g(x) = 1 x2
4.(d)
f(x) =
sin3(2x + 1)
4.(e)
h(x) =
x3
4.(f)
e x x
g(x) = x
e x
Find
dy
x 2 1
for the exercise x2y2 + 4y = 5 by using indicated differentiation.
dx
Page 8
6. At noon ship A is 200 km west of ship B. Ship A is sailing north at 40 km/hour while ship B is sailing
north at 25 km/hour.
A
2
Give
a
formula
for
D
in
terms
of
x
and
y.
(a)
D
x
B
y
200 km
dx
and
dy
, x , y and D when the duration is 6:00 p.m.
(b)
What are the computes of
(c)
What is the scold of diversify of the dissimilarity D between the ships at 6:00 p.m.
dt
dt
7. The magnitude of a round balloon is V =
4
r 3 .
3
Page 9
When the radius is 10 cm the radius is increasing at the scold of 2 cm/sec (
What is the scold of growth in the magnitude (
8.
dV
dr
2)
dt
) when the radius is 10 cm.
dt
A compatriot has 1000 feet of sheet; he wishes to environ a crosswise area, partitioned into 4 as
shown adown.
y
x
(a) Use the aloft knowledge to experience an countenance for y, in conditions of x.
(b) Experience a mathematical formula for the area of the rectangle in conditions of x.
(c) What compute of x gives the climax area for the aloft rectangle
9. Experience the provisos of the aftercited using L’Hospitals Rule.
Page 10
(a)
(b)
3
lim x 2 27
x3 x 9
4
lim x 2256
x 16
x4
(c)
lim sin x cos x 1
x0 sin x cos x 1
(d)
lim x ln(x)
x0
10. The exercise f(x) = x3 – 3x + 7.
Page 11
(a) For what seasons is the exercise f(x) increasing and decreasing?
(b) Where are the topical max and min , if they await?
(c) When is f(x) excavated up, excavated down and where are the summits of inflexion, if they await?
11. A compatriot has 100 feet of sheet, he can use a fabric on one edge but he must circumscribe the other three
sides. What are the magnitude of the rectangle PQRS that has the highest area.
S
P
y
x
Q
R
Page 12
12. The derivative f (x) cos x 4x 2 , if you are as-well told that f(0) = 2.
Find a exercise f(x) that has all these properties.
13. Use the aftercited knowledge
f (1) 2 , f (3) 6
g'(1) 1 , g'(2) 3
m(x) = f(x)g(x) ,
f (1) 4 and f (3) 10
g(1) 3 and g(3) 1
f (x)
r(x) =
and p(x) = f(g(x))
g(x)
To experience m'(1), r'(1) and p'(1)
Page 13
Page 14
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