The following function is injective or not?  s : C → C, s(z) = z^2 (Note: C means the complex number)

Q: find all complex soultions of 2x2+x+6=0

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Q: (a) Factorise z° + 1 over the real numbers.

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Q: indeterminate forms?

A: Indeterminate form is an expression involving functions whose limit cannot be determined from the…

Q: Let (x1, y1) = (7, 2) and (x2, y2) = (1, -1). Find √[(x2 - x1)2 + (y2 -y1)2]. Express the answer in…

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Q: 7. Differentiate f (x) = 9cot- (). Use exact values. You should simplify the complex %3D fraction.…

A: Topic:- derivatives

Q: Determine whether the function f(x) = 3x2 +2x f:R → R is a bijection. If it is not, explain why not.…

A: The objective is to determine whether the function is a bijection. fx=3x2+2x−5

Q: )х, х(0) 5 8 -1 -2 X(0) = X' = %3D X(t) = || %3D

A: To find: The value of x(t) Given information: x'=8-156xand the initial condition is x(0)=-26.…

Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: (2)に z8-92-3 %3D

A: We reduce the equation.

Q: give 4 real life examples of bijection

A: A function f: A to B is said to be bijective if it is  both one to one  and onto. A function f: A to…

Q: What are all the roots of f(x) = x* – 3x³ +x – 32 A -1, 3 only 1 ti3 only 2 1tiV3 -1, 3, 2 1, -3, VI…

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Q: x = 141+√ 14821 230 -,x== 141-14821 230

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Q: 6. Show that when 0</z - 11 < 2, Complex Analysis (z-1)" (2-1)(2-3)=-3 (2- #=() 2(z-1)

A: Here we prove this statement by using series expansion.

Q: Explain the other notation which is commonly used for ak in the Newton form of the interpolating…

A: The Newton interpolation polynomial are calculated as: \

Q: symmetri

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Q: Assume that y represents a positive real number. What is the conjugate of Vy - 24?

A: y-24

Q: Determine all values of x that make the expression %3D X-5 true. Show your work in the space…

A: We have to find value of x

Q: By means of Lagrange interpolation foomula, prove that 0.3 | -3 where (*)R = *R %3D

A: Given :- By means of Lagrange interpolation formula, y1 = y3 - 0.3 y5 - y-3 + 0.2y-3 - y-5 where yx…

Q: True or false: The scalar multiple -4A is obtained by multiplying each element of A by -4…

A: A quantity which have magnitude only is called scalar quantity, but the vector quantities have both…

Q: Prove that Σ", (2i-1)-. .

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

Q: 8. What are all the roots of the function f(x) = (x² + 1)(x – 2)? ? 2. -1 and 2 iand 2

A: solve for x over the real numbers (x^2+1)(x-2)^2=0 Split into two equations  (x-2)^2=0 or (x^2+1)=0…

Q: 17) Explain why these two quotients are different. Compute each one. (x – 2)* x* - 16 and X-2 x- 2

A: (a-b)2= (a-b)(a-b) and a2-b2=(a-b)(a+b)…

Q: tan X Select the rules - Alyebra -Recierocal -Quotien4 Py tuagoren ) Oda lE ver -Evaluation 58idate…

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Q: The real part of sech (2-j3) is -3.7245 -3.5906 O 0.0403 O -0.0106 -0.5309 1.0357

A: The Euler's formula is widely used formula in complex analysis. It makes a bridge between the…

Q: Show that Rsta is Hausdorff.

A: Note that a topological space X,I is said to be Hausdorff if (and only if) for every distinct points…

Q: Please find the roots of the equation f(x) = 3e-x - 4x + 1 using Bisection and False-Position…

A: Answer is mentioned below

Q: 5. y' = 2x?y – 4y %3D

A: 5 Given differential equation is y'=2x2y−4y......1. We have to find the solution of the given…

Q: Explain with examples what is meant by the indeterminate form 0/0.

A: To explain about the indeterminate form 0/0

Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: Find the inverse funclion of 5/2 FO)=(2x2 on the doman X20

A: Given function is f(x)=2x52  domain x≥0 find inverse of f(x)

Q: What are the roots of the function f(x) = x³ + x² − 7x -3? O 3, 1+√2, 1-√2 O -3,-1+√2, 1-√2 O 1, 3,…

A: Solution :-

Q: ) List all the possible rational zeros of flx) = 2r - 5x + 2x + 6 A) 2, ±3, 26 * 21, 2, 23 ±1, C)…

A: Topic = Algebra

Q: What is the difference between the minor of an element aij and the cofactor of the element?

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Q: Gven that Pe3 -3 3 f On Compore

A: 3. Given that, P=52337-1, Q=5-31237. (i) Obtain the value of PQ as follows.…

Q: A³ f2 = V³ fs 3

A:

Q: Can you tell me if I'm getting the right answers for -7π/4? Also, what am I supposed to say for the…

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Q: 2tanß 1-tan²B

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Q: Find the degree homogeniety of y'=2xy/y^2-x^2

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Q: 28. Express xg - x as a product of irreducibles over Z2.

A: The given polynomial is x8-x. This can be written as x8-x=xx7-1.

Q: What is the domain of { (z,3z2- 5) Iz ER except 0}? All real numbers All negative numbers {x\x€R>0}…

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Q: O OMS Bookmants y= 2x + 1

A: topic - slope intercept form y= mx +c is a slope intercept form where m is slope and c is y…

Q: What is rhe third root of unity ?

A: This question can be solved using the concept of complex numbers.

Q: Find dr/dtheta for theta^(-7/9) + r^(-7/9) = -5

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Q: Show that0+0iis a ‘complex additive identity element’; andthat1+0iis a ‘complex multiplicative…

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Q: What are all the possible rational roots of 2x^3 + 3x^2 - 10x + 4 = 0?

A: Given: - The equation is, 2x3+3x2-10x+4=0 To find: - The rational roots of the given equation.

Q: 3. Let 7, r, and r, be the roots ofx' +3x-5x-4= 0, construct the equation whose roots are: 7(r, +r3…

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Q: If x is a n-700 as a. always b. real number Sometimes never such that 1x11, then x" -> -0

A: We want to find correct answer.

Q: find the Doman (De) and The funcdia y= 2-

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Q: Sketch the nullcline for: x' = 4 - y2 + x2 Explain.

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Q: Find the inflection points of ƒ(x) = 4x* + 38x' – 30x² + 15. (Give your answers as a comma separated…

A: Our Aim is to find the inflection point of f(x)=4x4+38x3-30x2+15 -(i)

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.