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Concept explainers
Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review.
Problems 2–6 refer to the following polynomials:
(A) 3x – 4 (B) x + 2
(C) 2 – 3x2 (D) x3 + 8
5. What is the degree of each polynomial?
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Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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- 3) Compute where C is the circle |z― i| = - 1 2 2+1 Po z z - 2)2 dz traversed counterclockwise. Solution: TYPE YOUR SOLUTION HERE! INCLUDE A SKETCH OF THE COM- PLEX PLANE AND THE CURVE C. ALSO, MARK ALL SINGULARITIES OF THE INTEGRAND!arrow_forward2) Consider the function f (z = re²) = e cos(In(r)) + ie¯* sin(ln(r)). Show that is holomorphic at all points except the origin. Also show that =arrow_forward3) If a is a positive number, what is the value of the following double integral? 2a Love Lv 2ay-y² .x2 + y2 dadyarrow_forward
- 2) Consider the set SL(n, R) consisting of n x n matrices with real entries having de- terminant equal to 1. Prove that SL(n, R) is a group under the operation of matrix multiplication (it is referred to as the Special Linear Group).arrow_forward1) What is the parity of the following permutation? (1389) (24) (567)arrow_forward4.7 Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h²) to estimate the first derivative of the function examined in Prob. 4.5. Evaluate the derivative at x = 2 using a step size of h = 0.2. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.arrow_forward
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