Problem 3: For each of the two graphs below, determine whether they are planar. Justify your answer: if the graph is planar, show its planar embedding. If a graph is not planar, use Kuratowski's theorem to justify it. G h H h

Q: 6)- (-1)우. %3D

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Q: 1 Imit |2 – x| x → 2

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Q: Identify the zero's

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Q: State the Remainder Theorem.

A: Statement: If f(x) is divided by (x-a) then the remainder will be f(a).

Q: IsP2 spanned by 1 + x, x + x2,1 + x2?

A: To Show: Is P2 spanned by 1+x,  x+x2, 1+x2 ? Concept: Let V be a vector space and let S=v1, v2, v3,…

Q: As 00, y Select] As a -00, y Select J [ Select ]

A: Estimate by the graph where y approach as x approach to infinity

Q: Explain the two types of finite differences?

A: In this question, we have to explain the two types of finite differences.

Q: Multiply (w-5) and Cil w? _v=9)

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Q: Describe Fundamental Theorem of Linear Algebra.

A: Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating…

Q: Find x and y such that,  77815x - 8216y=(77815 , 8216

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Q: If P, be a polynomial of degree n, i.e., P, = aok" + a;k"-1. + a, then A" P. = aon!.

A: We have to solve given problem:

Q: lim 6+ -3

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Q: State and give an example of Mean Value Theorem

A: The objective is to state and give an example of Mean Value Theorem.

Q: Find the first 3 Maclaurin polynomials?

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Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

Q: 3 2 -4 - -47 1 -3 1 6 -2

A: We will find  the required.

Q: Define Conjugate transpose.

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Q: Calculate the commutators [p(hat)x3, x(hat)].

A: We have to calculate the following commutators. p^x3 , x^ Introduction: Commutation of operator A^…

Q: Define identity properties

A: Here we have to define the Identity properties:-

Q: Use the Conjugate Pairs Theorem

A: Given: Use the Conjugate Pairs Theorem

Q: Define the Newton form of the interpolating polynomial?

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Q: Define the Quotient Rule?

A: Let both u and v are functions of x then the derivative of (u/v) is: This rule is called the…

Q: x* +5х + 5х + 27 х+3

A: We need to simplify x4+5x2+5x+27x2+3. So,…

Q: 20 o o

A:

Q: 3 2uv 2uv

A: Definition used -        We know -                          a0=1aman=am-n

Q: Discuss the properties of polynomials

A: