Following are the test for Functions
(a) (i) The relation should be one-one or many-one, and (ii) Every first element is mapped which means that every pre-image should have an image. (b) For graphs: Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a function. If it cuts in more tha..
(a) (i) The relation should be one-one or many-one, and (ii) Every first element is mapped which means that every pre-image should have an image. (b) For graphs: Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a function. If it cuts in more tha..Note 1:
We say that f(x) is continuous if f(x) is continuous at every point in its domai..
Example:
Show that the function has a removal discontinuity at x = 4. Redefine the function f(x) at x = 4 to make it continuo..
Show that the function has a removal discontinuity at x = 4. Redefine the function f(x) at x = 4 to make it continuo..
..
Example:
In the first quadrant, as x approaches zero from the right of zero, the value of f(x) increases without bound. It becomes greater than any assigned positive real value. In this case, we say or Similarly, in the third quadrant as x approaches zero from the left, the value of decreases witho..
In the first quadrant, as x approaches zero from the right of zero, the value of f(x) increases without bound. It becomes greater than any assigned positive real value. In this case, we say or Similarly, in the third quadrant as x approaches zero from the left, the value of decreases witho..Limits
But we are interested in finding the value of y near 2. When x = 1.9, y = 3.9 x = 1.99, y = 3.99 x = 1.999 y = 3.999 . . . . . . Similarly, when x = 2.1 y = 4.1 x = 2.01 y = 4.01 x = 2.001 y = 4.001 . . . . . . Observe that as x approaches 2, y approaches 4. 4 is called the limit of f(x) as ..
But we are interested in finding the value of y near 2. When x = 1.9, y = 3.9 x = 1.99, y = 3.99 x = 1.999 y = 3.999 . . . . . . Similarly, when x = 2.1 y = 4.1 x = 2.01 y = 4.01 x = 2.001 y = 4.001 . . . . . . Observe that as x approaches 2, y approaches 4. 4 is called the limit of f(x) as ..See what our Users say :
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