9:51 R² x=(x)) ва налів P 1 g(x) = (0,0) kit homotopy from fto homotopy from of g to

Q: (a) A function p(x) with domain (0,8) that has p' (x) > 0 everywhere, p" (x) = 0 for all æ 4. 4 2 4…

A: Given domain of p(x) is 0,8.

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: for 0<x < 3, Let f(2) = {- (z – 3) (x – 3) for 3 < x < 6. Compute the Fourier cosine coefficients…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: can you explain how you got (x-2)=(t-3) and can you explain how you got the new limits because the…

A: Given:

Q: What is the B of f(x, y) = tan (x3³+ 2xy)? [sec ² (x²y³+ 2xy] (3x²y² +2x) [sec² (x²y³ + 2xy ] (+²+*+…

A:

Q: (@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

A: To explain why the given function is entire, given function is: fz=5z4−6+zcosz−z3ez

Q: if the Legendre polynomials P.(x) = -1 then: Find 1) ,x* P,(2) dx 2)P'(-1) A) L P.) dx = and P,(1) -…

A:

Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

A:

Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

A:

Q: Find all the singularities of tan(z) f(z) = determine their types, and compute the residues at the…

A: Given function is fz=tanzz. We have to find the singularity of fz. Now, limz→0fz=limz→0tanzz00…

Q: Q2 Find fr and fy for the following funetion: f(x,y) = + In(5x – 3y).

A: We find value of fx and fy of given function f(x,y)

Q: 1+(1+z²)/² • [a)] Show that csch 1 z = ln [(b)] Use part (a) to find all the values of csch (2i)

A: