Introduction :
The online calculus courses is common and open to everyone around the world. Students from anywhere can enroll in this online calculus courses. There is no need of class meetings in online calculus courses. Online calculus courses include limits, derivatives, applications of derivatives, integrals and application of integrals. In online calculus courses, students can attend final exam at their home or anywhere around the world. Derivatives and integrals are explained below with its applications to show how online courses helpful to you.
Derivatives and its applications:
In derivatives, we will study the changes in the values of y corresponding to small changes in the values of x where y and x are related to each other by the equation y = f(x).
Application of derivatives:
Example problem:
Find the derivative of the function y = 2x^3 + x^2 + 3.
Solution:
Step 1: Given function
y = 2x^3 + x^2 + 3
Step 2: Differentiate the given function y = 2x^3 + x^2 + 3 with respect to ' x ', to get `(dy)/dx`
`(dy)/dx` = 6x^2 + 2x
Understanding definition of parabola is always challenging for me but thanks to all math help websites to help me out.
Integrals and its applications:
Integration is the reverse process of that of differentiation. The process of finding derivative of the given function is called differentiation whereas finding the function whose derivative is known is called integration. This function is called as integral of the given function.
Application of integrals:
Example problem:
Find the integration of the function, f(x) = 3x + 8.
Solution:
Step 1: Given function
f(x) = 3x + 8
`int` f(x) dx = `int` 3x + 8 dx
Step 2: Separate the integral function
`int` 3x + 8 dx= `int` 3x dx + `int` 8 dx
Step 3: Integrate each function with respect to ' x',
`int` 3x + 8 = `(3x^2)/2` + 8x + C
The online calculus courses is common and open to everyone around the world. Students from anywhere can enroll in this online calculus courses. There is no need of class meetings in online calculus courses. Online calculus courses include limits, derivatives, applications of derivatives, integrals and application of integrals. In online calculus courses, students can attend final exam at their home or anywhere around the world. Derivatives and integrals are explained below with its applications to show how online courses helpful to you.
Derivatives and its applications:
In derivatives, we will study the changes in the values of y corresponding to small changes in the values of x where y and x are related to each other by the equation y = f(x).
Application of derivatives:
- Rate of change of quantities
- Errors and approximation
- Rolle's and Lagrange's theorem
- Maxima and minima functions
- Increasing function and decreasing functions
- Tangents and normal
- Optimization
- Graph shape
Example problem:
Find the derivative of the function y = 2x^3 + x^2 + 3.
Solution:
Step 1: Given function
y = 2x^3 + x^2 + 3
Step 2: Differentiate the given function y = 2x^3 + x^2 + 3 with respect to ' x ', to get `(dy)/dx`
`(dy)/dx` = 6x^2 + 2x
Understanding definition of parabola is always challenging for me but thanks to all math help websites to help me out.
Integrals and its applications:
Integration is the reverse process of that of differentiation. The process of finding derivative of the given function is called differentiation whereas finding the function whose derivative is known is called integration. This function is called as integral of the given function.
Application of integrals:
- To find area under simple curves
- To find areas of circles
- To find areas of parabolas
- To find areas of ellipses
- To find area between the curves
- Average function value
- Volumes of solids of revolution
Example problem:
Find the integration of the function, f(x) = 3x + 8.
Solution:
Step 1: Given function
f(x) = 3x + 8
`int` f(x) dx = `int` 3x + 8 dx
Step 2: Separate the integral function
`int` 3x + 8 dx= `int` 3x dx + `int` 8 dx
Step 3: Integrate each function with respect to ' x',
`int` 3x + 8 = `(3x^2)/2` + 8x + C
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