Definition of derivative, relate it to the slope of the tangent of a curve, derivative of the sum, difference, product and quotient of functions Differentiation relates to the measurement of change. For a linear function such as y = mx + b where b is the y-intercept and m is the constant slope. Here m … Read more

Trigonometric functions are continuous at all points Tangent and secant are flowing regularly everywhere in their domain, which is the combination of all exact numbers. Let a be a real number in the domain of a given trigonometric function, then $\lim _{x\to a}\sin x=\sin a$ $\lim _{x\to a}\cos x=\cos a$ $\lim _{x\to a}\tan x=\tan a$ … Read more

Let p be a polynomial function of x and c be a real number,the limit of p (x) as x approaches c does not depend on the value of f at x = c. It may happen, however, that the limit is precisely p (c).In such cases, the limit can be evaluated by direct substitution … Read more

You have already known that there is a very little difference between exponential and logarithmic functions. It is however important to recognize the most suitable ways to deal with these. Now, you may already know that the domain of a function is the set of probable inputs and also known as the x values. Also, … Read more

As mathematical approach to prove so many things, the mathematical induction plays a huge role and in the most possible way it’s important for proving the natural numbers’ property (n). As per mathematical induction principle, X(n) property is same for all the natural numbers – 0,1,2,3, ………n. Now, considering the given statement X (n), it … Read more

Since you may be dealing with functions and relations, it would certainly be important to make out the best ways to deal with the identification of their domain and range. Exponential functions and logarithmic functions are known to be very closely tied to one another since a log or logarithm is just another way of … Read more

Modulus function or absolute value function is said to be the one that consists of algebraic expressions that are enclosed within various absolute value symbols. Now, you must be aware of the fact that the absolute value of a number is determined by its distance from zero on the number line. Domain and range of … Read more

Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. Proofs by Induction In this section, we’ll be learning about the mathematical induction which proves that a specific statement holds true for all the integers that are positive. Now, first let’s make a rough guess at … Read more

Function’s domain is defined as the particular set values that an independent variable contained in a function can accept the work. The range exists as resulting values which a dependent variable can hold a value of ‘x’ changes all through the domain. For Cosine and Sine Functions, the Range and Domain There are no limitations … Read more

Since you may be focusing a better grip on functions and relations, it is absolutely important to take a look at suitable operations with rational functions. What is a rational function? A rational function is said to be the one that could be written down as the quotient for two polynomials. For instance, consider a … Read more