Calculus is the study of change and it is a vital topic of Mathematics. Integral calculus and differential calculus are two main branches of this topic. Differential calculus is concerned with rates of change whereas integral calculus gives information about the accumulation of quantities. Moreover, these branches are connected with each other in respect of fundamental theorem. It is stated that calculus was founded in the 17th century and since then; its concepts have been applied in many sectors including engineering, science, economics, computer science, medicine and others. Moreover, calculus is referred as the part of modern Mathematics. Students are suggested to learn this topic in a step-by-step manner.

Calculus is quite extensive and it has three parts like ancient, medieval and modern calculus. Limits, derivative applications, solid of revolution are some important sub-topics that students should learn thoroughly to get a thorough understanding in this topic. Some students find calculus tough and in that case, they are suggested to take online calculus help. TutorVista provides constructive and informative sessions for calculus. To avail these online sessions designed for calculus, students need to follow some easy steps. They can choose their sub-topics and can take sessions at their preferred time. Moreover, they can take assistance in solving assessments and homework, as well.

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- Functions Limits and Continuity
- Differentiation
- Differential Equations
- Indefinite Integrals
- Definite Integrals
- Applications of Derivatives
- Exponential and Logarithmic Series

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Calculus is added in the syllabus of higher school students. Moreover, TutorVista has experienced tutors and they give online personalized sessions as per the studentsâ€™ convenience. College calculus is not easy to deal with but the expert virtual tutors associated with TutorVista make it simple and easy in all manners.

Below are some examples based on calculus:

f(x) = sin x ... (1)

f(x + h) = sin (x + h) .....(2)

Subtract equation (1) from equation (2), we get

f(x + h) - f(x) = sin(x + h) - sin x

= 2 cos ($\frac{2x+h}{2}$) sin ($\frac{h}{2}$) [ using identity sin A - sin B = 2 cos($\frac{A+B}{2}$) sin ($\frac{A-B}{2}$)

= 2 cos (x + $\frac{h}{2}$) sin ($\frac{h}{2}$)

$\frac{f(x + h) - f(x)}{h}$ = $\frac{1}{h}$ (2 cos (x + $\frac{h}{2}$) sin ($\frac{h}{2}$))

= $\frac{2 cos (x + \frac{h}{2}) sin (\frac{h}{2})}{2 \times \frac{h}{2}}$ [ Because $\frac{sin \frac{h}{2}}{\frac{h}{2}}$ ]

= cos(x + $\frac{h}{2}$)

$\lim_{h\rightarrow0}$ $\frac{f(x + h) - f(x)}{h}$ = $\lim_{h\rightarrow0}$ cos(x + $\frac{h}{2}$)

= cos x

=> Derivative of sin x is cos x.

Given: $\int$ $\frac{log\ x}{x}$ dx

Substitute log x = t, then $\frac{1}{x}$ dx = dt

Now $\int$ $\frac{log\ x}{x}$ dx = $\int$ t dt = $\frac{t^2}{2}$

After re-substituting the values, we have

$\frac{(log\ x)^2}{2}$

More topics in Calculus | |

Rate of Change | Derivatives |

Differentiation | Integration |

Continuity | Discontinuity |

Calculus Homework Help | Cauchyâ€“Riemann Equations |

Entire Function | Removable Singularity |

Related Topics | |

Math Help Online | Online Math Tutor |