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Determine the value of the following series $\sum^{\infty}_{n=1}(\frac{4}{n^2+4n+3}-9^{-n+2}4^{n+1})$ Solution To determine their value, we must check if the series is a…

What is the difference between $\frac{dy}{dx}$ and $\frac{d}{dx}$ in Calculus? In Calculus, when we write $\frac{dy}{dx}$, it means we are differentiating the function $…

Proving the Madhava-Leibniz series for pi(π)  One of the earliest known approximations of $\pi$ was done by an Indian mathematician Madhava of Sangamagrama during th…

Why does pi have a constant value of 3.14159265359...?  can we define other values for pi?  $\pi$ is a lowercase greek letter used as a mathematical constant pronounced …

Find the second derivative of $y=\sqrt{3x^2-2x+1}$ By indices $y=(3x^2-2x+1)^\frac{1}{2}$ We use chain rule to evaluate $y$.  Formula $\frac{dy}{dx}=\frac{dy}{du}\times…

Why study calculus in real analysis when we can study it in elementary mathematics? Real analysis is an area of analysis that studies concepts such as sequences and thei…

Economical Calculus: Price inflation and the value of money One of the applications of calculus is in economics, calculus can be used to determine price inflation…

Linear Approximation Of Functions Given a function $f(x)$,if $x=a$ then the linear approximation of $f(x)$ is given by $L(x)=f'(a)(x-a)+f(a)$ Examples Use Lin…

Differentials of Functions for any function $f(x)$ that is differentiable,we defined $y=f(x)$ so that $\frac{dy}{dx}=f'(x)$ and the differential is given as $dy=…

JAMB past questions on Calculus below are some of the calculus questions from the previous jamb examinations, i believe you should have basic background of calculus,we…

Definition of Analytic Functions i) A complex function $f(z)$ is said at a point $z_0$, if $f$ is differentiable not only at $z_0$ but at every point of some neighborho…

Below are few calculus  Questions which  I solved..  (1)Find the derivative of the following if: (i) 2y²=x²siny+xy³ (ii)x²y²+4xy+x-6y=2 (2)differentiate y=cos-¹(4x³-1) (…

A qoutient function is a function expressed in terms of division for exam a/b. Hence in differentiation any function expressed in terms of qoutient are usually evaluat…

Here we give a little bit more difficult example of the product formula of differentiation.. We can see clearly that the first function here (x³+2)² is not a function we…

The product rule is simple and very interesting to use.. All you need to do is to define your given functions in terms of the variables of the product formula. You fir…

Example 2: find the derivative of (3χ²+4x)⁴ Solution : we simply use chain Rule because the function is defined in terms of powers. Chain Rule formula : dy/dx= dy/…

Rule 2: the chain Rule This rule is quite simple and easy it defined by: dy/dx= dy/du × du/dx To carry out chain Rule in any given function then that function must b…

differentiation is simple  in fact we can say  it's the simplest aspect or topic of mathematics.. But to carry out differentiation we need to know the rules. Rule1:…