1. Use the residue theorem establish the identity: 1 et + e- -da = t|2 플

Q: acosx+bx sinx-5 (ii) Find the values of a and b so that lim exists and finite

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Ei Tan Bo Xx SiA find JEi de a Bo

A: Given           εi=Tan β0X1X2β1-sin Yi3 Find ∂εi∂β1 and ∂εi∂β0.

Q: 7. Evaluate using the residue theorem eir dx x2 +1

A:

Q: Q1/: a: Using the relation showthat Jv2 (x) =, cos x

A: See the attachment

Q: use Theorem to find 31) F(A) = 4t? 5 Sin 34

A: To find the Laplace transform of the below function using the theorem. ft=4t2−5sin3t

Q: 5. lim (2x² – 5x + 1) x-1 A. 8 В. -8 C. -1 D. DNE

A: We can find the answer as below.

Q: (d) tan¹(x)dr

A:

Q: Simplify the following functions using Boolean algebra and its identities. List the identity used at…

A:

Q: Evaluate by Residue Theorem/Formula do where a = your registration number first digit, (a + bcos0)²…

A: It is clear that : cosθ=z-1zzdθ=dziz For the given integral ,…

Q: Show thatI cos ve (-1/4s)

A:

Q: Let fx) e sinx. Calculate and simplify f "(r)

A: Compute the second derivative for the given f ( x ).

Q: State the set of zeros of f(x)=2sin(x)cos(x) using set builder notation.

A:

Q: x² – 4 Evaluate: A =Vx2-4+ sec-스)+C ⑥ -Vx2-4+2 sec-스)+C =V x2 – 4 – 2 sec + C (D =2Vx2-4+ sec-1스)+C…

A:

Q: 9. Prove the following algebraic identity: (a - b)(a? + ab +b?)=a' -b'

A:

Q: show that there is a root of sin(x2)=e2-2.

A: To show that there is a root of sin(x2)=e2-2.

Q: Zero(s) of multiplicity one: Zero (s) of muit iplicity jwo Żerols) of muitnpncitj inree:

A: multiciplicity is no of times repetation of zeros that is known by putting given equation to zero.

Q: Use a local quadratic approximation to approximate tan 61⁰

A:

Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

A: Given function is  Fx=∫1xsin2tdt

Q: prove that theta(2m) = theta(m) when m is odd and theta(2m) = 2 theta(m) when m is even

A: We can start by using the definition of theta notation to prove these statements. Recall that theta…

Q: z f(z)=- at z=1 (z-1)"(z-2)(z-3)

A: Pole:- Let z0∈S and limz→z0fz does not exist, then z0 is called pole of order m, for some positive…

Q: Yn+1 = ayn-p+YYn-h (yn-h) 9-¹+8 +6

A: Given: The information showing the proof of a specific theorem.To prove: yn+1=αyn-p+γyn-hyn-hq-1+δ…

Q: Express as a sum.(sin ax)(cos bx)

A: Given : (sin ax)(cos bx)

Q: 1 + X tanh (x) 1 In 2 - 1 - X

A: The solution is given as

Q: aim(-4) 3) lim - -16 16-1) + lim++ sin(v

A: According to L Hospital's rule, if f(x) and g(x) are two differentiable function and limx→cf(x)g(x)…

Q: 4. Find The coefficient of the x’term in the Maclaurin polynomial for sin(2x)

A:

Q: a) Evaluate r(금). r(0)

A: According to our company policy, we are supposed to answer the only first question. For the rest…

Q: Determine the exact function value of cosh (In 2).

A: The given function is  Cosh(ln2)

Q: с) V (и-у) - и х(Vху) - ух(Vxи)- (и-V)у+(ү-V)и %3D

A:

Q: If a, ß be the roots of m (x-x)+ 2mx +3 = Q and m,m, be the two values of m for which a, B are…

A: