Classify the singularities of each of the following functions and find the corresponding residues: (a) f(z) = - Z (b) sin² z (c) zez-1 sin²;

Q: Differentiate f (x) = vx from first principles. %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: a. f(x) = V3x3 – 2 %3D b. y = (Vx + 1)(x² – x) 2x5-3 c. f(x) cos x d. y = sin(4x²)

A: All the questions are solved below.

Q: Q:Findthe domain of the following functions sin 'x (1) s''x (i) [x] 1 (ii)- | x | ,× cos 'x

A: In this question, we need to find the domain of the given functions.

Q: Find minimum of sin(x + 3) – sin(x + 1) – 2 cos(x + 2) where a E R.

A:

Q: Match each of graphs (A) and (B) in Figure with one of the following functions: (i) f(x, y) = (cos…

A: Given: i) fx,y=cosxcosyii) gx,y=cosx2+y2

Q: Find f′′(0) if f(x) = sinh−1(π2 + x2).

A:

Q: 2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].

A: Given that     g(t) = 8t[(2t+1)2+t]

Q: f2(x) = (4x + 5)°, fa(x)= (2x² +x)VI, fa(x) cos(3r) – 2 sin? x, COS

A:

Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

A:

Q: Þ(x, y(x)) = x² + 5y¹(x), where y(x) = sin(x). Find different methods and compare: a) Substitute for…

A:

Q: Consider the following pair of equations: x² + 2xy + z² = 1, sin(x) + y²z=1 What does the implicit…

A: Given system of equations: x2+2xy+z2=1,sin(x)+y2z=1 Point of interest: (x, y, z) = (0, 1, 1)

Q: a. Compute the derivatives of the following function: sec(xy) = 4x(3x+ 5)5 b. Find an equation for…

A: Product Rule of differentiation : d(u.v)dx=u.dvdx +dudx.v dxndx = nxn-1 Equation of line passing…