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In a sample of 500 people in Rajastan , 280 are rice eaters
and the rest are wheat eaters. can we assume that both rice and
wheat are equally popular in this district at 1% level of significance?
Determine whether the following series converge:
∑_(k=1)^∞〖(-1)〗^(k+1) (k+3)/(k(k+1))
Define the relation of d on A by xdy if x is contained within y. For
example, 01d101. Draw a digraph for this relation.
using the exterior angle inequality prove the sum of the measures of any 2 angles of a triangle is less than 180.
Let F(x, y) be the statement "x can fool y," where the domain consists of all people in the world. Use quantifiers to express each of these statements.
Prove in detail the following mappings from R to R
Let R be the set of real numbers
Φ1: R→R^+
Ф1= { (x, e^x); x ∈R}
Φ2: R→R^+
Φ2= { (x, α^2); x∈R}
Identity mapping
iA: A→A
α: Z→Z
α(n)=2n
in the following a set V, a field F, which is either R or C, and operations of addition + and scalar multiplication . , are given for alpha element of F and x element of V, we write their multiplication alpha × x as alpha • x, cheak whether V is a vector space over F, with these operations .
Find the Hermite interpolating polynomial for the function f(x) = √x satisfying the conditions H5(xi) = √xi, i = 0, 1, 2 and
′1
H5(xi)=2√x, i=0,1,2forthepointsx0 =1,x1 =4andx2 =9.
i
Reduce the polynomial to its natural form.
(a) Using the formula Tn(x) = cos(n cos−1 x), n ≥ 0, find the Chebyshev
polynomials T0(x), T1(x), T2(x), T3(x), and T4(x).

Q: Evaluate the following integral using residue theorem

∫z^2 e^z dz ; C : |z| = 1


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