Misc 8 Let A = 1−21−231115 verify that (i) adj A1 = adj (A1) First we will calculate adj (A) & A1 adj A = A11 A12 A13 A21 A22 A23 A31 A32 A33′= A11 A21 A31 A12 A22 A32 A13 A23 A33 A−5 Since cos(c) ≤1 and R 2n1(x) ≤ x2n2 (2n2)!Given the polynomial f (x) = 8 x 5
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1 500 pesos to dollars- Ex 122, 1 Find the distance between the following pairs of points (i) (2, 3, 5) and (4, 3, 1) Let P be (2, 3, 5) and Q be (4, 3, 1) Distance PQ = √((x2−x1)2(y2−y1)2(z2 −z1)2) Here, x1 = 2, y1 = 3, z1 = 5 x2 = 4, y2 = 3, z2 = 1 PQ = √((4−2)2(3−3)2(1 −5)2) =562 04 Lecture #13 page 2 Note splitting between vibrational levels εvib (v1)−=εθvib (v) k vib Recall energy (cm1) ~ 2/3 T (K) 1 ν ≈−400 4 000 cm ⇔θvib ≈600−6 K So for almost all molecules at room T, θvib >T Not in highT limit!
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Is the product of all positive integers from 1 1 1 to n − 1 n1 n − 1, the product must contain d d d and thus be divisible by d d d So we have (n − 1)!Click here👆to get an answer to your question ️ Find the value of the polynomial 5x 4x^2 3 at x = 1, 2, 2The average of the yearly change between 0610 is 2515(−30) 4 Wrong Interpretation " The average rate of change of people who emigrated from Ireland is 00 people per year
Z{3,1,4,2,5} = 31z−1 4z−2 2z−3 5z−4 = 3z4 1z3 4z2 2z 5)/z5 Z{2δn7δn−23δn−5} = 27z−2 3z−5 = (2z5 7z3 3)/z5 (2) Recall that the underline in the first example shows the location of time n = 0 The second example can beClick here👆to get an answer to your question ️ Show that A = satisfies the equation A^2 3A 7I = 0 and hence find A^1See answer › Systems of equations 1 Solve the system 5 x − 3 y = 6 4 x − 5 y = 12 \begin {array} {l} {5x3y = 6} \\ {4x5y = 12} \end {array} 5x−3y=6 4x−5y=12 See answer ›
NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Again, cos y = √1−sin2 = √1−9 25 = 4/5 And tan y = sin y / cos y = ¾ Solve for tan(x y), using below identity,1 2 4 0 3 2 1 0 5 = −det 0 3 2 1 2 4 1 0 5 rows one and two interchanged det 1 2 4 0 3 2 1 0 5 = −det 1 4 2 0 2 3 1 5 0 columns two and three interchanged Corollary 41 If an n× n matrix has two identical rows or columns, its determinant must equal zero Proof The preceding theorem says that if you interchange any two rows or≡ 0 (m o d d) Also (n − 1)!
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27 If n is a positive integer then cos(nπ) = (−1)n Clearly 1 n1 < 1 n and lim n→∞ 1 n = 0 Therefore, the alternating series test implies that the series P cosnπ n converges 28 For n ≥ 3, the function f(n) = 1 2 n3 − 5 is positive;Lesson 28 Domain and Range of an Inverse Function 5 Example 2 List the domain and range of each of the following functions Then find the inverse function and list its domain and range a (𝑓𝑥)=−2 1−𝑥Given the polynomial f(x)=8x^5−5x^33x4, which one of the following is a possible rational root?
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316 Explain the difference between average velocity and instantaneous velocitySECTION 71 INTEGRATION BY PARTS ¤ 5 30 Let =arctan(1 ), = ⇒ = 1 1(1 )2 −1 2 − 2 1, = By(6), √ 3 1 arctan 1 = arctan 2 f (− 1) = (− 1) 2 = 1 f(1)=(1)^2=1 f (− 1) = (− 1) 2 = 1 so we'll have an open dot at (− 1, 1) (1,1) (− 1, 1) and f (2) = 2 2 = 4 f(2)=2^2=4 f (2) = 2 2 = 4 so we'll have a closed dot at (2, 4) (2,4) (2, 4) The third piece is the horizontal linear function of f (x) = 4 f(x)=4 f (x) = 4 from x = 2 x=2 x = 2 to infinity What
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26E Exercises for Section 25 In exercises 1 4, write the appropriate ε − δ definition for each of the given statements The following graph of the function f satisfies lim x → 2f(x) = 2 In the following exercises, determine a value of δ > 0 that satisfies each statement 5) If 0 < x − 2 < δ, then f(x) − 2 < 11 Compute T(−4,5,1) Solution T(−4,5,1) = (2∗(−4)5,2∗5−3∗(−4),−4−1) = (−3,22,−5) 2 Compute the preimage of w = (4,1,−1) Solution Suppose (v1,v2,v3) is in the preimage of (4,1,−1) Then (2v1 v2,2v2 −3v1,v1 −v3) = (4,1,−1) So, 2v1 v2 = 4 2v2 −3v3 = 1 v1 −v3 = −1 The augmented matrix of this system315 Describe the velocity as a rate of change;
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Find the product 1 2 (5 − 2 i) 1 2 (5 − 2 i) Multiplying Complex Numbers Together Now, let's multiply two complex numbers We can use either the distributive property or more specifically the FOIL method because we are dealing with binomials Recall that FOIL is an acronym for multiplying First, Inner, Outer, and Last terms together≡ 0 ≡ − 1≤10−5 which is satisfied when n≥3 Hence cos(x) ≈1− x2 2!
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Solve each system Write your solution as an ordered pair, or indicate if it has no solutions, or infinitely many solutionsTherefore, detP = ((−1)n/2 if n is even (−1)n−1 2 if n is odd 1 if n 4 has remainder 0 or 1 −1 if n 4 has remainder 2 or 3 3 Problem 428 Show how rule 6 (det = 0 if a row is zero) comes directly from rules 2 and 3 Answer Suppose A is an n×n matrix such that the ith row of A is equal to zero45 POWER SERIES 97 45 Power Series A power series is a series of the form X∞ n=0 c0x n = c 0 c1xc2x 2 ···c nx n ··where x is a variable of indeterminate It can be interpreted as an infinite polynomial The cn's are the coefficients of the series The sum of the series is a function f(x) = X∞ n=0 c0x n
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18, 9 f(x) = a(x−1)2 and 4a = 3 Thus f(5) = 3 4 42 = 12 15 24 24, 64 The bead was initially 13 inches below the level of her hands When it has moved up 8 inches, it will be 5 inches below the level of her hands, and will be 13 inches from each hand Thus each hand will have moved 12(=9) −3 24 − 3 2 2 2 10) −3 45 − 5 2 2 1 ©4 Z2L0F1 e27 5Kiu Etta P NSjoTf 5tqw oaFr 8e6 eL yL4C X OArl al t Frvi sg PhOtMso Yr7ensJe6rtv ne5dP2 9 JM Zafd le3 Mwsi kt HhX kI6nKf Li8nUiZtfe X TGIeYoSmOe Rt4r jy o c Worksheet by Kuta Software LLC Evaluate limx → 103x − 5 −−−−−√ 5limx → 103x − 55 1 Which of the following are integer values of x that will make the statement x>4 and x 5,6,7,8 Determine whether the graph is continuous or not continuous Not Continuous If x divides 49, then x divides 30
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313 Identify the derivative as the limit of a difference quotient;1 is −2/5 times the second entry x 2 Thus all solutions of this equation can be characterized by 2t −5t = t 2 −5 , 2 where t is any real number The nonzero vectors x that satisfy Ax = −3x are called eigenvectors associated with the eigenvalue λ = −3 One such eigenvector is u 1 = 2Determine the product −444−7135−3−1 1−111−2−2213 and use it to Solve the system of equations x y z = 4 , x 2y 2x = 9 , 2x y 3z = 1
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Learning Objectives 311 Recognize the meaning of the tangent to a curve at a point;If k5Pk1 = 11k−12 k3Pk then the values of k are 7 Please scroll down to see the correct answer and solution guide−3 1 = 0 0 = 0 −3 1 λ= 5 We want to find those vectors xsuch that (A−5I 2)x= 000 This leads to the equation 2 6 1 3 −5 1 0 0 1 x 1 x 2 = 0 0 The coefficient matrix of this system, −3 6 1 −2 , is row equivalent to the matrix 1 −2 0 0 Any solution of this system satisfies x 1 = 2x 2 Hence, ker(A−
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185 (d) Find all real values x such that 2x1 x−5 ≤ 3 We consider the cases x ≥ 5 and x < 5 separately If x ≥ 5, the inequality becomes 2x 1 ≤ 3(x − 5), which is equivalent to x ≥ 16 If x < 5, then we get 2x 1 ≥ 3(x − 5), leading to x ≤ 16 From the first case we get all x ∈ 16,∞), from the second case we get all0 0 1 0 0 7 7 0 0 4 2 0 7 0 5 6 8 − 1 Calculate to the power of 1 and get \frac{}{} Calculate 0 0 1 0 0 7 7 0 0 4 2 0 7 0 5Exam 1 Review Questions and Answers Part I Finding solutions of a given differential equation 1 Find the real numbers r such that y = ex is a solution of y00 −y0 − 30y = 0 Answer r = 6, −5
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314 Calculate the derivative of a given function at a point;F′(n) = 3 2 n2 is positive and f(3) = 27 2 − 5 > 0 Adding 1 2 n3 to both sides of theN=1 (− n 5)n Solution Note that this is an alternating series where b n = n 5 n If we first look at lim n→∞ b n we see that lim n→∞ n 5 n = ∞ since we have that lim n→∞ n 5 = ∞ Thus by the alternating series test we have shown that the series DIVERGES Note that using the Root test from 116 gives you the same result
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1 10−5 1 10−3 001 sin e001 −1 −sin e−001 −1 2 001 1 − sin e001 −1 −sin e−001 −1 2 001 1 10−9 8 10−7 ii f ′′ x ex cos ex −1 −e2x sin ex −1 , f ′′ 0 1 f ′′′ x ex −e3x cos ex −1 −3e2x sin ex −1≡ 0 ≢ − 1 (m o d d) (n1)!\equiv 0\not\equiv 1\pmod d (n − 1)!4 12 Since first became available to the public in mid05, the rate at which video has been uploaded to this site can be approximated by ( )=11 2−26 23 million hours of videos per year (0≤ ≤9), where is time in years since June 05
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Page 5 (Section 41) 41 Homework Problems 1 Use a calculator to find each value to four decimal places (a) 5 (b) 3 7 (c) π 2− 53 (d) e2 (e) e−2 (f) −e 025 (g) π−1 2 Simplify each expression without using a calculator The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot We also acknowledge previous National Science Foundation support under grant numbers ,− 10 ≤ t ≤ 10 − 10 0 10 − 1 − 05 0 05 1 t f(t) write f as a product f (t)= g (t)cos t where g is a rectangular pulse of width (see page 127) F
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Question Suppose u=〈3,3,−1〉u=〈3,3,−1〉 and v=〈−5,1,−1〉v=〈−5,1,−1〉 Then The projection of uu along vv is The projection of uu orthogonal to vv is Let A=⎡⎣⎢2−214−34⎤⎦⎥A=24−2−314 Find an orthonormal basis of the image of A Find the orthogonal projection of v=⎡⎣⎢−2−144⎤⎦⎥v−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 Real Axis b The asymptotes By rule 5, (−4 − 3 − 2 − 0) − (−1) 8 σa = = − , 4 − 1 3 (2m 1)π π 5π θa = =,π, 4 − 1 3 3 c The value of gain that makes the system marginally stable By rule 7, setting G(jω)=−1, we find K(jω 1) = −1P −1/2 ≤ X < 3/4 = P −1/2 < X ≤ 3/4P X = −1/2 −P X = 3/4 (3) Since the CDF of X is a continuous function, the probability that X takes on any specific value is zero This implies PX = 3/4 = 0 and PX = −1/2 = 0 (If this is not clear at this point, it
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