Test for Functions (Summary)
The relation should be one-one or many-one, and Every first element is mapped which means that every pre-image should have an imag..
calculating area with pre algebra
Before describing the limits of trigonometric functions, we state few theorems along with Sandwich theorem, which helps in calculating a variety of limits in subsequent chapter..
3. Onto function
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..One-one function
Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. {(1, 4), (2, 4), (3, 4), (4, 5)} Here, one image has three pre..
Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. {(1, 4), (2, 4), (3, 4), (4, 5)} Here, one image has three pre..Example 4:
Plot the graph of 5x-2y=5. Use the graph to find the area between the line and the axe..
Examples:
i) Because the element c A is not associated with an element of B. ii) Because the element a A has no unique association. Hence y = f(x), y is called the image of x and x is called the pre-image of..
i) Because the element c A is not associated with an element of B. ii) Because the element a A has no unique association. Hence y = f(x), y is called the image of x and x is called the pre-image of..Function
Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresp..
Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresp..Function Function - Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element ha..
Function - Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element ha..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..Proof:
Consider a circle with centre O and radius r. Join AB. Let the tangent at B meet OA produced at P. Draw BN perpendicular to OA. From ONB, BN = r sin q From OBP, BP = r tan q From the figure, we have Area of triangle OAB < Area of sector OAB < Area of..
Consider a circle with centre O and radius r. Join AB. Let the tangent at B meet OA produced at P. Draw BN perpendicular to OA. From ONB, BN = r sin q From OBP, BP = r tan q From the figure, we have Area of triangle OAB < Area of sector OAB < Area of..See what our Users say :
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