1 Find and classify the • [(a)] ' isolated singularities and zeros of sin 3z f(z) = Justify your answer. z(ez + 3) Find the Laurent expansion 3z • [(b)] ' of f(z) = in the domain z2 – 2z – 8 2 < |z| < 4.

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

A:

Q: Problem Let a = V3+ v7. (a) Find a degree 6 monic polynomial in Q[x] having a as a root. (b) Prove…

A:

Q: Let Tn(x) denote the Chebyshev polynomial ofdegree n and defineUn−1(x) = 1/nT'n(x)for n = 1, 2, . .…

A: Definition:

Q: (10') Use Rouche's theorem to find the number of roots of 2z4 – 5z + 1 = 0 (1) for |z| < 1 (2) for…

A:

Q: Let f (x), −L < x < L, be an odd function that satisfies the symmetry condition f (L −x) = −f (x)…

A: Given: Let us consider the given function fx, -L&lt;x&lt;L and the condition fL-x=-fx. To find: An=0…

Q: 6. Let P be a non-zero polynomial such that P(1 + x) = P(1 – x) for all real x and P(1) = 0. Let m…

A: Here we have been given that P is a non-zero polynomial such that P(1+x)=P(1-x) for all real x and…

Q: The Gamma Function I (n) is defined by I (n) = xn-le-ªdx,n > 0. (а) Find Г (1), Г (2), and Г (3).…

A: We will show the given results.

Q: iscuss the singularities and poles of ze sinz f(z) (z-2)(z²-1)²(z²+5z+6)(z+7)(z²+4)'

A:

Q: Find f(f(f(1))) given 2 + 3 if x 5 f(F(f(1))) =|

A:

Q: 4- (a) Show that XYX = -Y and (b) show that [XY,YZ] = -2iY.

A: a) To show that XYX = -Y, we can use the definition of the commutator [X,Y] = XY - YX and the…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.