1. a. Evaluate the following limit: lim ?→4 ( 2? 3−128 √?−2 ) (8
marks) b....
1. a. Evaluate the following limit: lim ?→4 ( 2? 3−128 √?−2 ) b. Find the number ? ???ℎ ?ℎ?? lim ?→−2 ( 3? 2+??+?+3 ?
2+?−2 ) exists, then find the limit
1. . Find the limit: lim ?→ ∞ (? + √?2 + 2?)
2. If 1200 ??2 of material is available to make a box with a square
base and an open top, find the largest possible volume of the
box.
2. The volume of a right circular cone is ? =1/3 ??^2 ℎ , where ?
is the radius of
the base and ℎ is the height.
(a) Find the rate of change of the volume with respect to...
(a) Find the limit of the following functions:
-lim as x approaches 0 (1-cos3(x)/x)
-lim as x approaches 0 (sin(x)/2x)
-lim as theta approaches 0 (tan (5theta)/theta)
(b) Find the derivative of the following functions:
-f(x) = cos (3x2-2x)
-f(x) = cos3 (x2/1-x)
(c) Determine the period of the following functions:
-f(x) = 3 cos(x/2)
-f(x)= 21+ 7 sin(2x+3)
1. Evaluate: (a+b)/(c-d) + 9/(a+d) when a=5,
b=3, c=8, d=4
a. 6
b. 3
c. 15/2
d. 17/13
2. Solve for x: 5(x+3) = 35
a. 2
b. 7
c. 4
d. -4
3. Acid rain occurs primarily as a result of
a. operating a nuclear power plant
b. burning coal or oil containing sulfur
c. by-products created by operating an oil refinery
d. the use of Freon and other refrigerants
4. The "ozone holes" at the polar region arise...
a) Evaluate the limit lim x→0 tan(2x) / x
b) Differentiate y = x^tan(x)
c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4
at the point (1, 2).
d) Differentiate f(x) = arctan(x^2 + 1)
e) Differentiate f(x) = ln(cosh x)
Thank you!
From this Sample
No A. B.
1. 7. 4.
2. 8. 5.
3. 9. 3.
4. 5. 6.
5. 7. 2.
6. 6. 4.
Test of hypothesis for difference of two means by using
1. t Test
2. ANOVA
Take 5% type 1 error, then compare the results.
Show that t² is equal to f.
A graphing calculator is recommended.
For the limit
lim x → 2 (x3 −
3x + 8) = 10
illustrate the definition by finding the largest possible values
of δ that correspond to ε = 0.2 and ε =
0.1. (Round your answers to four decimal places.)
ε = 0.2
δ =
ε = 0.1
δ =
A graphing calculator is recommended.
For the limit
lim x → 2 (x3 −
2x + 4) = 8
illustrate the definition by finding the largest possible values
of δ that correspond to ε = 0.2 and ε =
0.1. (Round your answers to four decimal places.)
ε =
0.2
δ =
ε =
0.1
δ =