Top

# Calculus Help

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.

## Topics Covered in Calculus

Some essential topics are mentioned below and these are thoroughly covered by our online program:
• Functions Limits and Continuity
• Differentiation
• Differential Equations
• Indefinite Integrals
• Definite Integrals
• Applications of Derivatives
• Exponential and Logarithmic Series

Get personalized attention and solve complicated calculus problems with experienced Math tutors and understand all these topics in a detailed manner. In short, get well-geared learning help online.

## Get Calculus Homework Help

Calculus homework help is well-designed in all manners as this is prepared under the supervision of proficient academicians. Students can get calculus homework help at their convenient time and make their learning process easier and worthy. Students can choose their topic and most importantly, they can get repeated sessions on each topic. Free online sessions are also available for each Math topic.

TutorVista designs suitable online sessions for Math topics. Moreover, experienced tutors are available 24 x7 and they assist students in solving each calculus problem in an accurate manner. Understand each calculus topic and improve your score in exams. Moreover, students can choose regular homework help, as well. Free question banks are also available online. Get instant online help with experienced tutors and brush up your subject knowledge before exams.

## College Calculus Help

Get unlimited online calculus tutorials from TutorVista. Our online tutors are well-experienced and they solve each problem in a thorough manner. Most importantly, these virtual tutors are available 24x7 and hence, students can connect with them whenever they need help. Our calculus tutors are well-trained and they guide students in a systematic manner. However, solve your homework and assignments by taking adequate help from TutorVista. Understand step-by-step explanations and make all complex calculus problems easy.

Calculus is added in the syllabus of higher school students. Moreover, TutorVista has experienced tutors and they give online personalized sessions as per the students’ 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:

### Solved Examples

Question 1: Find the derivative of f(x) = sin x using first principles.
Solution:

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.

Question 2: Solve $\int$ $\frac{log\ x}{x}$ dx

Solution:

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 Cauchy–Riemann Equations Entire Function Removable Singularity
*AP and SAT are registered trademarks of the College Board.