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
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