Skip to content
**Ashish Kumar - let's learn**, implement then understand Maths and Physics
# 13. Limits and Derivatives

## Select Lecture

Advertisements

The biggest risk is not taking any risk. In a world that’s changing really quickly, the only strategy that is guaranteed to fail is not taking risks. – Mark Zuckerburg

The expected value of the function as dictated by the points to the left of a point defines the left hand limit of the function at that point. Similarly the right hand limit.

Advertisements

Limit of a function at a point is the common value of the left and right hand limits, if they coincide.

For a function f and a real number a, \(\lim_{x \to a} {f(x)}\) and f(a) may not be same (In fact, one may be defined and not the other one).

For functions *f* and *g* the following holds:

Advertisements

\( \lim_{x \to a} [f(x) \pm g(x)] = \lim_{x \to a}f(x) \pm \lim_{x \to a}g(x) \)

\( \lim_{x \to a} [f(x) \times g(x)] = \lim_{x \to a}f(x) \times \lim_{x \to a}g(x) \)

\( \lim_{x \to a} \frac{f(x)} {g(x)} = \frac {\lim_{x \to a} f(x)} {\lim_{x \to a} g(x)} \)

Following are some of the standard limits

\( \lim_{x \to a} \frac {x^n-a^n}{x-a} = n a^{n-1} \)

\( \lim_{x \to 0} \frac {\sin(x)}{x} = 1 \)

\( \lim_{x \to 0} \frac {1-\cos(x)}{x} = 0 \)

Advertisements

The derivative of a function f at a is defined by

\( f'(a) = \lim_{h \to 0} \frac {f(a+h)-f(a)}{h} \)

Derivative of a function f at any point x is defined by

\( f'(x) = \frac{d}{dx} f(x) = \lim_{h \to 0} \frac {f(x+h)-f(x)}{h} \)

For functions u and v the following holds:

Advertisements

\((u \pm v)’ = u’ \pm v’\)

\((uv)’ = uv’ + vu’\)

\( \left(\frac{u}{v} \right)’=\frac{u’v-uv’}{v^2} \) provided all are defined.

Following are some of the standard derivatives.

\( \frac{d}{dx} (x^n) = n x^{n-1} \)

\( \frac{d}{dx} (\sin x) = \cos x \)

\( \frac{d}{dx} (\cos x) = -\sin x \)

- New session will be from 1
^{st}April 2020 to 31^{st}March 2021. - The syllabus of Class 10 Maths, Class 11 Maths and Class 12 Maths will be completed in the new session.
- The following is the detailed list of new features and topics that will be provided to the members of our website throughout the new session.

- Course System for all the Chapters
- Low Resolution Videos (240p)

- Binary Operations Class 12 Maths Chapter 1
- Inverse Trigonometry Full Course Class 12 Maths Chapter 2
- Remaining Questions of Class 12 Maths Chapter 4
- Remaining Topics & Questions of Class 12 Maths Chapter 5
- Remaining Questions of Class 12 Maths Chapter 6
- Applications of Integrals Class 12 Maths Chapter 8
- Differential Equations Class 12 Maths Chapter 9
- Linear Programming Problem Class 12 Maths Chapter 12
- Probability Class 12 Maths Chapter 13
- Remaining Questions of Class 11 Maths Chapter 1
- Remaining Questions of Class 11 Maths Chapter 2
- Introduction to 3D Geometry Class 11 Maths Chapter 12
- Mathematical Reasoning Class 11 Maths Chapter 14
- Statistics Class 11 Maths Chapter 15
- Probability Class 11 Maths Chapter 16
- Solutions of Previous Year Question Papers Class 12 Maths
- Constructions Class 10 Maths Chapter 11
- Area related to Circles Class 10 Maths Chapter 12
- Surface Areas and Volumes Class 10 Maths Chapter 13
- Statistics Class 10 Maths Chapter 14
- Probability Class 10 Maths Chapter 15

- There could be more topics from NCERT Exemplar, Board’s Question Bank etc. but that would depend on the funds we would collect from the membership.
- The speed by which we would provide the above is completely depend on the funds we would collect from the membership.
- However,
**the above listed topics and features will be provided within the time frame of new session so that no student would face any difficulties.**

Advertisements

These membership offers will be made available soon on the website.

**Please note:**

- Due to unavoidable circumstance caused by Coronavirus epidemic, we are unable to provide online tuition as per the promised schedule.
- Agam Sir wants to provide you the best possible education that’s why he has decided to postpone the online tuition to the next year.
- He instructed us to inform all of you, so that his students will not face any difficulties because of the delays and they can make the suitable arrangements in time.
**There is no change in the membership of ₹158 per month.**

If you have not received support team’s emails then do the following

- Check Spam Folder for previous emails
- Add our support team Email ID support@ashishkumarletslearn.com in your contacts, so that future emails will not go to spam folder.