Extreme Value Theorem: If f is continuous on a closed interval [a,b] then f has both an
absolute maximum and minimum on the interval [a,b].
Mean Value Theorem: If y=f(x) is continuous on a closed interval [a,b] and is differential in [a,b]
then at least o
Find the function with the given derivative whose graph passes through the point p.
a) f(x) = cos(x) + sin(x) + 2, P(,3)
f(x) = -cos(x) + sin(x) + C
f() = -cos() + sin() + c = 3
F(x) = -cos(x)+sin(x)+2
b) f(x) = 1/x+3, P(-2,4)
f(x) = n(x+3)+c
A car accelerates from rest at the beginning of an entrance ramp. It accelerates at a steady rate
of 15ft/sec. The ramp is 300 feet long. How fast is the car going at the end of the ramp?
a(t) = 15
v(t) = 15t
s(t) = 7.5t=300
A particle starts at x=0 and moves with a velocity of v(t)=t+2. Where is the particle at t=3 sec?
Use 3 subdivision with LRAM, RRAM, and MRAM.
LRAM - 1(2+3+6) = 11 ft, Underestimate
RRAM - 1(3+6+11) = 20ft, Overestimate
MRAM - 1(2.25+4.25+8.25) = 14.75ft
The first biography of author Eudora Welty
came out in 1998 and she was 89 years old at
(A) and she was 89 years old at the time
(B) at the time when she was 89
(C) upon becoming an 89 year old
(D) when she was 89
(E) at the age of 89 years old
access to inside or privileged information about a
companys prospects uses that information in buying
or selling company shares.
(A) when a corporate officer who has access to
inside or privileged information about a
companys prospects uses that informati
companys prospects and he uses that
10 10 10 10 10 10 10
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Some or all parts of the following sentences are underlined.
The first answer choice, (A), simply repeats the
underlined part of the sentence. The other four choic
playground setting, it can be seen
(B) Having observed the interactions of preschoolers
in a playground setting, it can be seen
(C) If one observes the interactions of preschoolers
in a playground setting, you can see
(D) Observing the interactions of pre
(D) Atahualpa, and then there was a demand for
(E) Atahualpa, and then demanded ransom
13. Although demand for cars, motorcycles, and other
consumer goods are booming, the economy is
growing only at roughly 4 percent a year, and the
other consumer goods is booming
14. Samuel Sewall, who was a judge in the Salem witch
trials but later repented his role and, in 1700, wrote
the first attack on the American slave trade.
(A) Samuel Sewall, who was a judge in the Salem
witch trials but lat
other singers voices have
2. The mathematics teacher drew a right triangle on the
blackboard, he proceeded to demonstrate that we
could determine the length of the longest side of the
triangle if we knew the lengths of its two shorter
(A) The mathe
(D) it is important to concentrate on the things that
hurt us in life
(E) participating in sports provides a distraction
from the isolation of a writers life
19. How would the author of Passage 2 respond to the
author of Passage 1s viewpoint that a failur
Time20 Minutes is correct and blacken the corresponding choice on your answer
16 Questions sheet. You may use any blank space on the page for your work.
You may use a calculator whenever you think it will be helpful.
Use the diagrams provided to
it is highly fragile,
(C) Although the Ming vase is priceless and highly
(D) Because the Ming vase is priceless and highly
fragile is why
(E) Because the Ming vase is both priceless and
6. The soft, pulpy flesh of the passion frui
to develop flexibility and to become a more agile
(A) exercises to develop flexibility and to become
a more agile tumbler
(B) exercises for the development of flexibility and
to become a more agile tumbler
(C) exercises so that they develop flexi
minutes, the temperature rose from 8 to 7. What
was the average hourly increase in temperature?
(A) 5 (B) 7.5 (C) 10 (D) 15 (E) 22.5
3. For how many integers, n, is it true that n2 30 is
(A) 5 (B) 6 (C) 10 (D) 11
(E) Infinitely many
4. Which of
(A) 4 (B) 5 (C) 5.5 (D) 6 (E) 7
14. If y varies inversely with x and directly with z,
and x = 4 and z = 8 when y = 10, what is the value
of x + z when y = 20?
(A) 6 (B) 12 (C) 16 (D) 18 (E) 24
15. What is the average (arithmetic mean) of 330, 360,
intimate setting, appearing before smaller
audiences than most theaters today.
(A) appearing before smaller audiences than most
(B) they appeared before smaller audiences than
most theaters today
(C) appearing before audiences smaller than
(D) It represents a metaphor.
(E) It minimizes a liability.
17. The author finds it ironic that he tends to dismiss
most comparisons of athletics to art (lines 85 and
(A) athletics is the basis for great art
(B) he finds comparisons generally
diagram the battery VEE forward biases the EB junction while the battery VCC reverse
biases the CB junction.
As the EB junction is forward biased the holes from emitter region flow towards the base
causing a hole current IPE. At the same time, the electro
We know that IC = IB + (1+) ICBO where ICBO is the reverse saturation current. As the
temperature increases ICBO increases there by increase in IC and hence changing the Qpoint.
2. Current gain ()
In the process of manufacturing the transistors different
This d.c. voltage is called bias voltage.
As the input circuit has low resistance, a small change in the signal voltage Vi causes a
large change in the base current thereby causing the same change in collector current
(because IC = IB).
The collector curr
If emitter is open circuited, no charge carriers are injected from emitter into the base and
hence emitter current IE = 0. Under this condition CB junction acts a reverse biased diode
and therefore the collector current (IC = ICO) will be equal to the rev
is taken along y-axis and VCB is taken along x-axis. It is clear from the graph that the o/p
current IC remains almost constant even when the voltage VCB is increased.
i.e. a very large change in VCB produces a small change in IC. Therefore, output resist
source such as microphone to a level which is suitable for the operation of another circuit
as loud speaker. In such cases, amplifiers are used.
When amplifiers are cascaded, individual amplifiers provides required amplification and
input and output provi
Fig 3.5: p-n-p transistor operated in Cut-off region
When both EB junction and CB junction are reverse biased, the transistor is said to be
operated in cut-off region. In this region, the current in the transistor is very small and
thus when a transistor
In this configuration, base is used as common to both input and output. It can be noted
that the i/p section has an a.c. source Vi along with the d.c. source VEB. The purpose of
including VEE is to keep EB junction always forward biased (because if there