C. Calculus Formation
Relationship with Plaque:
* Calculus is formed by the deposition of calcium and phosphate salts in bacterial plaque. These salts are present in salivary and crevicular fluids. * Plaque mineralization begins within 24-72 hours and takes an average of 12 days to mature. * Calculus contributes to the disease by providing foci for plaque accumulation. It is not the causative or etiologic factor, plaque is. * Calculus is porous and can act as a reservoir or nidus of bacteria and endotoxin related to the disease process. * Calculus formation has been observed in germ-free laboratory animals but is far more abundant in similar germ-infected laboratory animals. The role of the bacteria in relation to calculus formation is not completely understood. Plaque is a soft, sticky accumulation that occurs on dental and various other intra-oral surfaces. It is the host to a complex micro-system of micro-organisms whose pathogenicity and virulence cause inflammatory diseases of the gingival & periodontal tissues. Plaque can be removed from tooth surfaces by direct brushing. It is possible to have a mouth with plaque but no calculus Calculus is formed by the deposition of mineral salts in plaque. It is hard and firmly adherent to the tooth surfaces on which it forms and it cannot be removed by brushing. Calculus acts as a focal point for plaque accumulation, a nidus of bacteria and hinders complete removal of plaque. It is almost impossible to have a mouth with calculus but no plaque. We remove plaque and calculus by instrumentation and home care to allow natural immunity to resolve the inflammation and restore health. Plaque Retention Factors

These are conditions that favor plaque accumulation and hinder plaque removal by the patient and the dental professional. Examples of these are: * Orthodontic Appliances
* Partial Dentures
* Malocclusions
* Faulty Restorations
* Calculus
* Deep Pockets
*...

...
Calculus in Medicine
Calculus in Medicine
Calculus is the mathematical study of changes (Definition). Calculus is also used as a method of calculation of highly systematic methods that treat problems through specialized notations such as those used in differential and integral calculus. Calculus is used on a variety of levels such as the field of banking, data analysis, and as I will...

...Portfolio in Calculus
Submitted by:
Chloe Regina C. Paderanga
Submitted to:
Sir Ferdinand Corpuz
Journal for the Month of June
WHAT I LEARNED?
I learned many things this month. It was good that our teacher repeated the topics in basic math to strengthen our foundation. Even if we had a hard time, I don’t see any reason why we should complain because I understand that our wanted to master these topics to be able to move to a higher math. The topics tackled...

...1. 7.5/8
The height in metres of a ball dropped from the top of the CN Tower is given by h(t)= -4.9t2+450, where t is time elapsed in seconds.
(a) Draw the graph of h with respect to time
(b) Find the average velocity for the first 2 seconds after the ball was dropped
h(0)=(0,450), h(2)=(2,430.4)
= (430.4-450)/(2-0)
= -9.8m/s √
(c) Find the average velocity for the following time intervals
(1) 1 ≤ t ≤ 4
h(1)=(1,445.1) h(4)=(4,371.6)
= (371.6-445.1)/(4-1)
= -24.5m/s √
(2) 1 ≤ t ≤ 2...

...No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Pre-requisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
9. 10.
Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear...

...
Calculus:
Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, Differential Calculus and Integral Calculus, which are related by the fundamental theorem of calculus.
Calculus is the...

...Calculus
is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of...

...INDETERMINATE FORMS AND IMPROPER
INTEGRALS
Deﬁnition. If f and g are two functions such that
lim f (x) = 0
x→a
and
lim g(x) = 0
x→a
then f (x)/g(x) has the indeterminate form 0/0 at a.
sin t
x2 − 9
Illustration.
has the indeterminate form 0/0 at 0 and
has the
t
x−3
indeterminate form 0/0 at 3.
Theorem. (L’Hopital’s Rule) Let f and g be functions diﬀerentiable on
an open interval I, except possibly at the number a on I. Suppose that for
Chapter 2: INDETERMINATE...

...CHALLENGING PROBLEMS FOR CALCULUS STUDENTS
MOHAMMAD A. RAMMAHA
1. Introduction In what follows I will post some challenging problems for students who have had some calculus, preferably at least one calculus course. All problems require a proof. They are not easy but not impossible. I hope you will ﬁnd them stimulating and challenging. 2. Problems (1) Prove that eπ > π e . (2.1) Hint: Take the natural log of both sides and try to deﬁne a suitable...

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