Continuity at a Point
1. We say that f(x) is continuous if f(x) is continuous at every point in its domain. 2. If f and g are two continuous functions then f + g, f - g, fg are continuous function..
Continuity at a Point
A function f (x) is said to be continuous at x = a ifA function f (x) is said to be continuous at x = a if f (a) exist..
A function f (x) is said to be continuous at x = a ifA function f (x) is said to be continuous at x = a if f (a) exist..Removal Discontinuity of a Function at a Point
If limit of a function f exists at a point c, but it is not equal to the value of the function at c. But if f(c) l, then the function is said to have removal discontinuity at x = c. This type of function can be made continuous by charging the value of f (c). If we change f(c) = l, th..
If limit of a function f exists at a point c, but it is not equal to the value of the function at c. But if f(c) l, then the function is said to have removal discontinuity at x = c. This type of function can be made continuous by charging the value of f (c). If we change f(c) = l, th..Step 3:
Choose a point that does not satisfy the inequation and shade the remaining parts leaving the line. If the point satisfies the given inequation, shade the part including the point and the line. The process of shading is clear from the graphs depicted abo..
Graphical representation of linear inequations on the real number line
A real number line can be used to represent the solution set of an inequation (Linear). The convention is that O (a hollow circle) marks the end of a range with a strict inequality (i.e. < or >) and (a darkened circle) marks the end of a range involving equality as well..
A real number line can be used to represent the solution set of an inequation (Linear). The convention is that O (a hollow circle) marks the end of a range with a strict inequality (i.e. < or >) and (a darkened circle) marks the end of a range involving equality as well..Theorem 10:
If f and g are real functions such that fog is defined, if g is continuous at a point c, and if f is continuous at g(c), then fog is continuous at ..
Limits (Contd....)
Limits at infinity: If x is a variable such that it can take any real value how much ever The two important properties of these one-sided limits that i) If the left hand limit and right hand limit of a function at a point exists, but are not equal, then we conclude that..
Limits at infinity: If x is a variable such that it can take any real value how much ever The two important properties of these one-sided limits that i) If the left hand limit and right hand limit of a function at a point exists, but are not equal, then we conclude that..Rectangular axes
The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axis. The point of ..
The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axis. The point of ..Example:
Find at least 3 sets of values for the variables satisfying the equation. 2x+y=5 Express y in terms of x. y=5-2x Select three values of x, find corresponding values of y. x=0, y=5-(2x0)=5 x=1, y=5-(2x1)=3 x=-1, y=5-(-2)=7 Draw the x and y - axes. Choose a suitable scale so as to locate the sel..
Find at least 3 sets of values for the variables satisfying the equation. 2x+y=5 Express y in terms of x. y=5-2x Select three values of x, find corresponding values of y. x=0, y=5-(2x0)=5 x=1, y=5-(2x1)=3 x=-1, y=5-(-2)=7 Draw the x and y - axes. Choose a suitable scale so as to locate the sel..Linear Equation Graphical representation
Rectangular axes - The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axis. The ..
Rectangular axes - The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. The horizontal number line is called x-axis and the vertical number line is called y-axis. The .. Result
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