2. a) द्वारा परिभाषित फलन f का प्रांत ज्ञात कीजिए।
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Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate.
a) The set is an infinite set.
b) The greatest interger function is continuous on .
c) .
d) Every integrable function is monotonic.
e) defines a binary operation on
, the set of rational numbers.
If , show that:
Hence find the value of .
वह प्रतिबंध ज्ञात कीजिए कि वक्र और
एक-दूसरे को लम्बवत् प्रतिच्छेद करते हैं।
यदि एक आय फलन द्वारा दिया गया है, जहाँ x निवेश है, तो अधिकतम आय ज्ञात कीजिए। यदि प्रारम्भिक आय 0 है, तो आय फलन R भी ज्ञात कीजिए।
वक्र और इसकी y-अक्ष के समांतर अनंतस्पर्शी के बीच का क्षेत्रफल ज्ञात कीजिए
If the revenue function is given by , x being the input, find the maximum revenue. Also find the revenue function R, if the initial revenue is 0.
b) Trace the curve , clearly stating all the properties used for tracing it.
The set of real numbers with the usual addition (+) and usual multiplication (.) is given. Define (*) on
as:
Is () associative in ? Is (.) distributive over (*) in
? Check.