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Remark
The value of the definite integral of a function over any particular interval depends on the function and the interval, but not on the variable of integration that we choose to represent the independent variable. If the independent variable is denoted by t o..
The value of the definite integral of a function over any particular interval depends on the function and the interval, but not on the variable of integration that we choose to represent the independent variable. If the independent variable is denoted by t o..Introduction to Differentiation
Introduction to Differentiation - After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter,..
Differentiation of Parametric Functions
If x=f(t) and y=g(t), where x and y are dependant on the independent variable t, then t is called the paramete..
If x=f(t) and y=g(t), where x and y are dependant on the independent variable t, then t is called the paramete..Limitations of Dimensional Analysis
Dimensional analysis has no information on dimensionless constants. If a quantity is dependent on trigonometric or exponential functions, this method cannot be used. In some cases, it is difficult to guess the factors while deriving the relation connecting two or more physical qua..
Statement
Some sentences depend on a variable for its truth value (i.e., true or false). e.g., "2+4+6+2n=2n" is true for n=1 but false for n=2, n=3 etc. As the above sentence is definitely true or definitely false for a particular positive integral value of n, the senten..
Uncertainty in Measurement
When dealing with objects that can be counted, one can always get an exact answer. But while measuring the weight of a person, the volume of milk in a container, the length of a cloth etc. it is not possible to measure them exactly. The difference in the two situations arises because objects are me..
Muscular Contraction
Muscle is composed of a large number of muscle fibres. The muscle fibres are arranged in groups. Each group is under the control of a single motor neuron, the axon of which sends a terminal branch to each fibre of the group. All the muscle fibres of a group contract when a nerve impulse travels dow..
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> as x tends to 'a' through values greater than 'a', then l 2 is called the right hand limit. Differentiation The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Ca..
Le Chatelier's Principle
The state of equilibrium in any system depends upon factors present in the system, such as temperature, pressure and concentration of various species. These factors are called reaction variables or parameters. A change in any one of the parameters may affect the position of the ..
Module Three: Anticipating Patterns
Probability: Interpreting probability, including long-run relative frequency interpretation 'Law of Large Numbers' concept Addition rule, multiplication rule, conditional probability, and independence Discrete random variables and their probability distributions, including bin..
Probability: Interpreting probability, including long-run relative frequency interpretation 'Law of Large Numbers' concept Addition rule, multiplication rule, conditional probability, and independence Discrete random variables and their probability distributions, including bin.. Result
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