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Showing posts with label limits. Show all posts
Showing posts with label limits. Show all posts

# CBSE Class 11 - Mathematics - Limits and Derivatives

Part-3  Algebra of Limits

In the previous post Limits and derivatives Part-2, we get basic ideas of the algebra of limits and also learned about rules and properties of limits.

Let us try to solve few problems:

Q1: Evaluate the given limit $\lim_{r\rightarrow 1} \pi r^2$

Answer: $\lim_{r\rightarrow 1} \pi r^2 = \pi(1)^2 = \pi$  # CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2)

In the previous blog post Limits and derivatives Part-1 , we learn

$\lim_{x\rightarrow a} f(x) = l$ and it is called limit of the function f(x)

The two ways x could approach a number an either from left or from right, i.e., all the values of x near a could be less than a or could be greater than a.

In this case the right and left hand limits are different, and hence we say that the limit of f(x) as x tends to zero does not exist (even though the function is defined at 0).  # CBSE Class 11 - Mathematics - Limits and Derivatives

Q1: Define Calculus.

Answer: Calculus is that branch of mathematics that mainly deals with the study of change in the value of a function as the points in the domain change.

👉Note: The chapter "Limits and Derivatives" is an introduction to Calculus.

👉Calculus is a Latin word meaning ‘pebble’. Ancient Romans used stones for counting.

Q2: Who are called pioneers of Calculus (who invented Calculus)?

Answer: Issac Newton (1642 - 1727) and G. W. Leibnitz(1646 - 1717).

Both of them were invented independently around the 17th century.

Q3: What is the meaning of 'x tends to a' or x → a?

Answer: When x tends to a (x  → a), x is nearly close to a but never equals to a.

e.g. x → 3 means the value of x maybe 2.99 or 2.999 or 2.999...9 is very close to 3 but not exactly equal to 3. Similarly, x may be 3.01, 3.001, 3.0001... from the right side and gets closer to 3.  