## Solve the Differential Equation (x^2+1)y’=xy

In this tutorial we shall solve a differential equation of the form $$\left( {{x^2} + 1} \right)y’ = xy$$ by… Click here to read more

From basic to higher mathematics

In this tutorial we shall solve a differential equation of the form $$\left( {{x^2} + 1} \right)y’ = xy$$ by… Click here to read more

In this tutorial we shall solve a differential equation of the form $$y’ = \frac{{\sqrt x }}{{{e^y}}}$$ by using the… Click here to read more

In this tutorial we shall solve a differential equation of the form $$y’ + \sqrt {\frac{{1 – {y^2}}}{{1 – {x^2}}}}… Click here to read more

Differential equations are frequently used in solving mathematics and physics problems. In the following example we shall discuss the application of… Click here to read more

Differential equations are commonly used in physics problems. In the following example we shall discuss a very simple application of the… Click here to read more

In the following example we shall discuss the application of simple differential equation in business. If $$P$$ is the principal… Click here to read more

In this tutorial we shall solve a differential equation of the form $$\left( {{y^2} + x{y^2}} \right)y’ = 1$$, by… Click here to read more

Let A and B be any two non–empty sets. Then a function ‘$$f$$’ is a rule or law which associates… Click here to read more

Example: Find the range of the function $$f\left( {\text{x}} \right) = \frac{{{\text{x}} + 1}}{{{\text{x}} – 1}}$$. Solution: We have \[f\left(… Click here to read more

Constant Function: Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘$$f$$’ from ‘A’ to ‘B’ is… Click here to read more

One – One Function: Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘$$f$$’ from A to… Click here to read more

Meaning of the Phrase “Tend to Zero”: Suppose a variable ‘x’ assumes in succession a set of values. \[1,\;\frac{1}{{10}},\;\frac{1}{{{{10}^2}}},\;\frac{1}{{{{10}^3}}},\;\frac{1}{{{{10}^4}}},\; \cdots… Click here to read more

Example: If $$f\left( {\text{x}} \right) = {{\text{x}}^3} – 2{{\text{x}}^2} + 3{\text{x}} – 7$$, then evaluate the limit $$\mathop {\lim }\limits_{{\text{x}} \to… Click here to read more

\[\frac{{{\text{dy}}}}{{{\text{dx}}}}\left( {\text{c}} \right) = 0\] \[\frac{{\text{d}}}{{{\text{dx}}}}\left( {{{\text{x}}^{\text{n}}}} \right) = {\text{n}}{{\text{x}}^{{\text{n – 1}}}}\] \[\frac{{\text{d}}}{{{\text{dx}}}}\left[ {{\text{c}}f\left( {\text{x}} \right)} \right] = {\text{c}}f’\left( {\text{x}}… Click here to read more

Example: Find $$\frac{{{\text{dy}}}}{{{\text{dx}}}}$$ if $${\text{y}} = \left( {2{{\text{x}}^3} – 4{{\text{x}}^2}} \right)\left( {3{{\text{x}}^5} + {{\text{x}}^2}} \right)$$ Solution: We have \[{\text{y}} =… Click here to read more

\[\frac{{\text{d}}}{{{\text{dx}}}}\left( {\sin {\text{x}}} \right) = \cos {\text{x}}\] \[\frac{{\text{d}}}{{{\text{dx}}}}\left( {\cos {\text{x}}} \right) = – \sin {\text{x}}\] \[\frac{{\text{d}}}{{{\text{dx}}}}\left( {\tan {\text{x}}} \right) =… Click here to read more

Example: Differentiate $$\frac{{\sqrt {\sin {\text{x}}} }}{{\sin \sqrt {\text{x}} }}$$with respect to ‘x’. Solution: Let $${\text{y}} = \frac{{\sqrt {\sin {\text{x}}} }}{{\sin… Click here to read more

The inverse process of derivatives is called anti–derivatives or integration. “A function $$f\left( {\text{x}} \right)$$being given and it is required… Click here to read more

1) $$\int {1dx = x + c} $$ 2) $$\int {adx = ax + c} $$ Where $$a$$is any constant…. Click here to read more

Evaluate: (i) $$\int {\left( {3{{\text{x}}^6} – 2{{\text{x}}^2} + 7{\text{x}} + 1} \right)} {\text{ dx}}$$ (ii) $$\int {\frac{{{{\text{t}}^2} – 2{{\text{t}}^4}}}{{{{\text{t}}^4}}}{\text{ dt}}}… Click here to read more

Example: \[\int {\frac{{{{\text{x}}^2} + 2\sqrt {{\text{x}} – 1} }}{{2{{\text{x}}^2}\sqrt {{\text{x}} – 1} }}{\text{dx}}} \] Solution: We have \[\int {\frac{{{{\text{x}}^2} +… Click here to read more