matte tnatitaie aeo analog? INTEGRAL CALCULUS
aepntimeiiiai (MATH 22)
LONG gurz #2:
lilatlamaiias 1 Quarter/2011-2012
I. zLTERNA'EVE RESPGNSE: Write T if the statement is True and F if
the statement is False. cfw_2 points each)
1. Applying the LIATE str
7 20. Which of the following has no horizontal asymptote?
x ,g x
a. f(x) = icDgU) :
x 1 x2 11
b. fix) = xi; :1. fix) = xii!
21. A circle with center at (-3, -2) passes through (1, 2). Find its radius.
a) 2d? b) 3J5 @245 d) 543
I 22. The directrix of
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32. What is the equivalent expression of cos (180 A)?
aisinA b)cosA c)sinA d) cosA
33. Solve for the value of x: xix! +3x10 :xZ.
5312 b) 3 c) 4 I d) 5
34. A man can do a certain job in 10 hours and his younger son can do it in 12 hours. A
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Illllarlmentot FINAL EXAMINATION
Mathematics 3. MATHZZCALCULUS 2
Mechanics 2'"l Quarter sv 2009-2010
I. EVALUATE EACH OF THE FOLLOWING INTEGRALS. Show your complete solutions. Final
answers should be in simplied fractional form
10. What is the behavior of the curve y = f(x) when y" is negative?
a) concave upward c) vertical
b) horizontal d) concave downward
11. The volume of a sphere is increasing at the rate of 6 cm3/hr. At what rate is its surface
area increasing when the ra
Manna Institute of Fesggiusv CALCULUS 2
ilaaartmemoi f 7x LOWTHUi)1b
Mathematics a ~Q
I. Choose the letter of the best answer (4 points each).
1. The integrand in the expression I 3x3 dx is
a) j b) x c) 3x2 d)dx
1-, Department of
,. . iMathematics and Mechanics $32: EQEQTEGRAL CALCULUS
fit M A l U A II C Ii N I Ii R - M A K A r i 2NDQTR2010-2011
DIRECTIONS: Please put all your things under your chairs. For each of the following
questions, Show all your complete s
cfw_.m Department of
4th. Quarter S.Y. 2010 2011
[email protected] Mathematics and Mechanics Integral Calculus
'3:_S/ m MATH22
I. TRUE or FALSE. Write TRUE if the statement is correct othenlvise write FALSE .(Zpoints each
1. The process of nding the
Hanna Institute at monument!
/ Ilenartmemni "
lst Quarter SY 2011-2012
Direction: Choose the best answer from among the given choices.
1. Which of the following is true at the inection point
OGIEAL nos-mum OF THE PHILIPPINES \B
g PH Y-SICS COMPETENCI' EXAM
E . _ _ - DATE: 9: - Eb
'. Cggggsg'gmis: SHADE. THE LETTER THAT H.
3 THE 5%qust To THE CORRECT mswea. PROVIDE
.3 0N FOR moment-somatic 0U BSnons.
l- A fmrormmz
Ii! H 1 2-H x 4'. I
A I 1 4 J lircle whose Circumferance lies on the points ( +2 , 1. t4 t '3 Mind (4 . 7 L
. . B. cfw_3,2 c. 15.2) - 3'
. Find the area hounded by the points ( -3 , 4),(-2,-1j, (4 , 4 J, and (0. 5 I.
A 27 units B. 15 units (2.
UNIT : 6 SOLUTIONS
When two or more than two substance mix and from a uniform or homogeneous mixture, Such a
mixture is called solution.
Type of solutions
The solutions can be found in three states; Solid, Liquid and Gas. The solute and s
Convex/Concave Lens Problem Bank
1. An object is 5.0 cm from a convex lens with a focal length of 6.00 cm. Locate and describe the image. [-30 cm;
virtual, erect, larger]
2. What focal length concave lens is needed to form a virtual image 10 cm from the l
Isomerism: Constitutional Isomers and Stereoisomers
Constitutional Isomers = same molecular formula, different
Stereoisomers = same molecular formula, same connectivity
of atoms but different arrangement of atoms in space
There are 4 types of Organic Reactions
An Introduction to Organic Reactions:
Acids and Bases
Intermediates In Organic Reactions
There are 4 Types of Organic Reactions
What did we learn in Chapter 4?
solute + solvent ! solution
empirical solubility rules:
Which ionic compounds are soluble in water?
strong electrolytes - soluble i