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±12. practice questions state whether the product of -2√3 and -2√5 is irrational. how do you find four rational numbers between 10 and 11? explain why the product of two irrational numbers may or may not be a rational number using suitable examples. learn more maths topics and get ...
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS) The value of f(0), so that the function f(x)=(1-cos(1-cosx))/(x^(4... 05:03 The jump value of the function at the point of the discontinuity of th... 04:11 f(x)=((4^x-1)^3)...
The spaces of polynomials of the previous section are replaced by the spaces of rational functions Ln=span{B0,…,Bn}. Note that if we set π0=1 and πn(z)=∏k=1n(1−ᾱkz), n⩾1, then f∈Ln is of the form p/πn with p∈Πn. The spaces of negative powers of z ...
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Example I.1.2 (Maths Practice ). Let's consider a basic case of a rational function: y = f (x) = 1 + x2 x2 − 2x + 1 (I.1.16) Firstly, for large values of negative and positive x, y ≈ 1, i.e. it tends towards a constant. In the case of Eq. (I.1.16), we ...
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