use the triangle inequality to show that if -2<x<1 then |x2 +x |<6
#2. Let n E N and X1,X2, ,yn, and zi,22, An be real numbers. ,An, yī,Y2, #a) Prove the identity #b) Use the identity in #a) to prove (the Cauchy-Schwartz inequality) that #1) Extend the result in #b) to prove that #d) Use the inequality in #b) to prove the inequality which is the triangle inequality
#2. Let n E N and X1,X2, ,yn, and zi,22, An be real numbers. ,An, yī,Y2, #a) Prove the identity #b) Use the identity...
#2. Let n E N and x1,x2,.., Xn, yı,y2,..,Ja, and zł,Zy, #a) Prove the identity An be real numbers #b) Use the identity in #a) to prove (the Cauchy-Schwartz inequality) that #1) Extend the result in #b) to prove that 4 #d) Use the inequality in #b) to prove the inequality which is the triangle inequality
#2. Let n E N and x1,x2,.., Xn, yı,y2,..,Ja, and zł,Zy, #a) Prove the identity An be real numbers #b) Use the identity in...
4. In this problem, you will give an algebraic proof of the triangle inequality. (a) Show that for any w, z EC, \w + zl2 = ww + (wz + wz) + zz (b) Show that 2Re(wz) < |w|. (c) Use the results of (a) and (b) to prove that [w + zl2 = ([w+ -12 and note how the triangle inequality follows from this one.
4. The solution of the inequality x2 – 4 < 0 is (a) –2 < x or x > 2 (b) –2 < x < 2 (C) x>-2 (d) x < 2 (e) None of the above 5. The domain of the function f(x) = V2is (a) (-2,2) (b) (-0, -2) U (2,00) (c) (-0, -2] U (2,0) (d) (-20, -2] U (2,00) (e) None of the above 6. The range of the function f(x) = 2 sin(x) is (a)...
6. (Bonus question: extra marks) Here we will show that ||p difficult property is the triangle inequality: ||la +b||p < || ||, + ||b||p . Here are the main steps: ( )P is a norm over J R" for p > 1.The only k-1 1 + q for a, b0 and 1 1. Prove Young's inequality: ab < b 19)/for any ak, bk E R and 2. Prove Holder's inequality: 1 lab (=1 |akP)"/? TI 1. You + k=1 can...
Solve the inequality f(x) <0, where f(x) = - x2(x + 4), by using the graph of the The solution set for f(x) <0 is. (Type your answer in interval notation.) function. Ay 4- 2- х 500 -8 -6 -4 -2 2 4. 6 -8- -104 -12-
Prove that the series expansion of the exponential function is
Cauchy.
please use triangle inequality.
Will rate, thank you
20 1 et = n! n-0
Apply Chebyshevs Inequality to lower bound P(O< X < 4) when E(X) 2 and E(X2)-5
17. The measures of two sides of a triangle are 8 and 14. Use an inequality to express the possible measures of the third side, m.
Let F, C R be defined by F.-{x | x 20 and 2-1/n-x2〈 2+1/n). Show that n-&メ2. Use this to show the existence of V2. 18.
Let F, C R be defined by F.-{x | x 20 and 2-1/n-x2〈 2+1/n). Show that n-&メ2. Use this to show the existence of V2. 18.