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In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n) < 2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases c) Proof: Inductive step setup. This is the beginning of the inductive step where you are stating the assumptions in the inductive step an what you will be proving in that step. As you do so, identify the inductive hypothesis.

In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n) < 2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases c) Proof: Inductive step setup. This is the beginning of the inductive step where you are stating the assumptions in the inductive step an what you will be proving in that step. As you do so, identify the inductive hypothesis.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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d) Proof: Inductive step
Transcribed Image Text:d) Proof: Inductive step
Q3 – Proof of Cost, In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n)<2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases. c) Proof: Inductive step setup . This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis.
Transcribed Image Text:Q3 – Proof of Cost, In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n)<2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases. c) Proof: Inductive step setup . This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis.
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