AK Shrivastav

Right from the time when a child starts his/her academics, the dilemma of choosing the board of education becomes a prime concern for parents. The choice of board makes a significant difference in the early development of the child and his/her exposure to the kind of education system that we have. In the Indian education system, two of the most recognized boards of education that one gets to opt for are CBSE and ICSE. The education system is split into primary, secondary and senior secondary levels. These levels play a significant role in building up one's career goals and achievements. The question that arises is what is better for the child? How does one choose the right system. One has to note that the two boards are very diverse and hence cannot be clubbed together. We need to examine the two boards on the basis of their functionality, offering abilities and other standards. CBSE is responsible for preparing the syllabus for the secondary and senior secondary levels. It is one the most preferred boards in India. It follows the national curriculum along with additional subject matter. The board conducts two examinations the All India Secondary School Examination, AISSE (Class X) and the All India Senior School Certificate Examination, AISSCE (Class XII). CBSE is recognized by the NCERT (National Council of Educational Research and Training) with the aim to operate a chain of central schools (Kendriya Vidyalaya) that could cater to the government employees who are in transferable jobs. A number of private schools have started to offer CBSE since a lot of private sector employees are also moving from place to place. The CBSE syllabus is very structured, highly predictable and controlled. All national entrance examinations are conducted as per this syllabus. ICSE on the other hand is conducted by yet another board, CISCE or the Council for the Indian School Certificate Examination. It is similar to AISSE conducted by CBSE. An offshoot of the Cambridge IGCSE that existed during the British regime was taken over by the Anglo Indian Board and is now governed by the Council for the Indian School Certificate Examinations. ICSE has taken in a lot of structures from the NCERT. At Grade 10, it is as of now is the toughest board examination. ISC (Class XII) is equally difficult to crack owing to its extremely detailed syllabus. Let us try to see the major differences between the two: Medium of Instruction: CBSE approves both English and Hindi language as the medium of instructions, ICSE does not recommend Hindi. Regular and Private Candidates: CBSE is affiliated to a large number of schools all over India. The board allows both regular candidates, who study in CBSE schools, as well as private candidates from non-affiliated schools to appear in the exams. Contrary to this, ICSE does not allow a candidate who has not been studying in an ICSE affiliated school to appear for the exams. Board Recognition: CBSE is recognized by Indian government and ICSE is not. Although the certificates provided by both of them are globally valid, yet CBSE has a better footing in the subcontinent than ICSE. CISCE is now recognized by many foreign education systems as equivalent to senior examination or high school. Curriculum/Course Content: The syllabus prepared by CBSE is more suitable for qualifying in various entrance examinations, including the medical and engineering professional exams. The syllabus of ICSE is more detailed and requires the student to remember a lot. CBSE is comparatively easier than ICSE. Both CBSE and ICSE (CISCE) have slightly different focus in terms of course content. CBSE is extremely focused on science and maths with a lot of attention paid to the application of knowledge. CISCE (ICSE) on the other hand is more balanced with equal focus on language, arts and science. Assessments: One more point of distinction between the two boards is the evaluation and assessment of students. In ICSE, internal assessments.

You see, 0^0 = 1, and it's obvious to a mathematician. The only problem is that the function f: [0, \infty) x R -> R, f(x, y) = x^y is discontinuous in (0, 0) and that's what causes problems -- for instance, this is the source of the whole "indeterminate form" notion. If a function f is continuous in (a, b), then for every two sequences a_n, b_n, such that lim a_n = a, lim b_n = b, we have lim f(a_n, b_n) = f(a, b). That's why lim (a_n)^(b_n) = a^b if (a, b) != (0, 0), and this is "determinate form". But if (a, b) = (0, 0), then no matter how we define 0^0, it does not follow that lim (a^n)^(b^n) = a^b = 0^0, because in this case, lim (a_n)^(b_n) can be every positive value, and so mathematicians used to call it "indeterminate form" (it's not common today, though). So, since this problem is unsolvable in a consistent (continuous) way, we define 0^0 = 1, to be consistent with exponentiation rules, at least. I've never seen a need for an "intuitive" explanation of exponentiation -- the usual definition is as intuitive as one can get. The thing is, most people do not know, _why_ expressions like pi^e are supposed to make sense -- they just take exponentiation as given. Only then they need to make up some explanation why "exponentiation rules" are like this, and what exponentiation is about. Hell, people don't even know what real numbers are! How are they supposed to make sense of exponentiation with exponent other than natural number?

It depends on what type of calculus problem it is! Differential Calculus has its own approach of domain and range and if it's clear enough then DC is yours Suman and Integration requires practice of different methods . Better if u ask me in which chapter of calculus you are facing problem so that I can help you out of that specific chapter or the topic .