Working Rule to Check Whether a Differentable Function is Increasing or Decresing
(1) Let the given function be f (x) on the real number line R. (2) Differentiate the function f(x) with respect to x and equate it to zero i.e., put f '(x) = 0. Solve for x. These values of x which satisfy f '(x) = 0 are called Critical values of the function (3) Arrange these Critical values in a..
Working rule for Evaluating Definite Integral with Suitable Substitution
Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Write and express in ter..
Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Write and express in ter..Step1:
We know that every polynomial function is continuous and product of continues functions are continuous. f (x), being product of polynomials of degree 1, is a continuous function in [4,10..
Derivative of a Function of a Function
Derivative of a Function of a Function - So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we d..
Derivative of a Function of a Function - So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we d..Rate of Change of Quantity
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to..
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to..Operation on Real Functions
The following are the Operation on Real Functions: Sum Function, Difference Function, Product Function, Quotient Function, Scalar Multiplication Function, Composite Functions, Inverse Function..
Rate of Change of Quantity
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect to x at x 0 . If y is a funct..
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect to x at x 0 . If y is a funct..Rate of Change of Quantity Rate of Change of Quantity - If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect ..
Rate of Change of Quantity - If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect ..See what our Users say :
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