DIFFERENTIATION OF STANDARD FUNCTIONS
CBSE Class 11 - Mathematics - Limits and Derivatives Part-10
You have learnt theorems of differentiation part-9. Let us proceed further. Here is a list of differentiation of some standard functions:
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CBSE Class 11 - Mathematics - Limits and Derivatives Part-10
You have learnt theorems of differentiation part-9. Let us proceed further. Here is a list of differentiation of some standard functions:
CBSE Class 11 - Mathematics - Limits and Derivatives Part-9
You have learnt about finding derivatives using the first principle in part-7 and part-8. Let us proceed further. Here is a summary of theorems on differentiation.
Differentiation |
Derivatives Using First Principle
Q1: What is the derivative of a function at a point?
Answer: Let y = f(x) is a continuous function. It means the value of y changes as the value of x changes.
At x = a, is a point in its domain of definittion. The derivative of f at a is defines as:
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: $\lim_{r\rightarrow 1} \pi r^2 = \pi(1)^2 = \pi$
Questions and Answers #class11Maths #Limits
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)
① 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.
② 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).
Part-1 - Questions and Answers
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.