help with functions limits and the derivative

Functions Limits and Continuity - The concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the valu..

The concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the values generated in the laboratory or collected in the f..

The derivative of the function f with respect to a variable x is the function f ' whose value at x is provided the limit exist..

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..

Derivative of a Function - So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute..

Let f be a function of x (y=f(x)). Let a be a point in the domain of f. The RHD of f at a is defined as where h>0, provided the limit exist..

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 dif..

Limits of Trigonometric Functions..

Left Hand Limit: Let f(x) tend to a limit l 1 as x tends to a through values less than 'a', then l 1 is called the left hand limit. Right Hand Limit: Let f(x) tend to a limit l 2 as x tends to 'a' through values greater than 'a', ..

Functions Limits and Continuity - Functions can be added, subtracted and multiplied. They can also be divided where the divisor function does not take the value zero. These operations create new functions.Functions can be added, subtracted and multi..