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Task 1 Count the number of vowels in a phrase using recursion only. You can think of this problem as "I can count the number of vowels in this phrase by counting the number of vowels in the first character, then counting the number of vowels in the rest of the phrase." We define a vowel as being A, E, I, O or U. This is one of those problems that can just as easily be solved with traditional programming structures such as a loop - but we're asking you to use recursion for the exercise. Consider: what replaces the loop structure? When will we stop recursion? Task 2 The constant e (Euler's number) is approximated by the following sequence: 1₁ 1+ + 1 1! 2! + ... + n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. We say that there is some value epsilon (e) such that, when the change in the approximation from one term to the next is less than said epsilon, we have reached sufficient precision. That is, when the term you're proposing to add is less than epsilon, you don't add it - you're already there. Write a recursive program to computer Euler's Number to an epsilon of 0.0000001 Check your results using an online tool like Wolfram Alpha. You will also need a helper method to compute the factorial of a number - this should also be done recursively.

Task 1 Count the number of vowels in a phrase using recursion only. You can think of this problem as "I can count the number of vowels in this phrase by counting the number of vowels in the first character, then counting the number of vowels in the rest of the phrase." We define a vowel as being A, E, I, O or U. This is one of those problems that can just as easily be solved with traditional programming structures such as a loop - but we're asking you to use recursion for the exercise. Consider: what replaces the loop structure? When will we stop recursion? Task 2 The constant e (Euler's number) is approximated by the following sequence: 1₁ 1+ + 1 1! 2! + ... + n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. We say that there is some value epsilon (e) such that, when the change in the approximation from one term to the next is less than said epsilon, we have reached sufficient precision. That is, when the term you're proposing to add is less than epsilon, you don't add it - you're already there. Write a recursive program to computer Euler's Number to an epsilon of 0.0000001 Check your results using an online tool like Wolfram Alpha. You will also need a helper method to compute the factorial of a number - this should also be done recursively.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Task 1 Count the number of vowels in a phrase using recursion only. You can think of this problem as "I can count the number of vowels in this phrase by counting the number of vowels in the first character, then counting the number of vowels in the rest of the phrase." We define a vowel as being A, E, I, O or U. This is one of those problems that can just as easily be solved with traditional programming structures such as a loop - but we're asking you to use recursion for the exercise. Consider: what replaces the loop structure? When will we stop recursion? Task 2 The constant e (Euler's number) is approximated by the following sequence: 1₁ n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. 1+ 2! + ... We say that there is some value epsilon (e) such that, when the change in the approximation from one term to the next is less than said epsilon, we have reached sufficient precision. That is, when the term you're proposing to add is less than epsilon, you don't add it - you're already there. Write a recursive program to computer Euler's Number to an epsilon of 0.0000001 Check your results using an online tool like Wolfram Alpha. You will also need a helper method to compute the factorial of a number - this should also be done recursively.
Transcribed Image Text:Task 1 Count the number of vowels in a phrase using recursion only. You can think of this problem as "I can count the number of vowels in this phrase by counting the number of vowels in the first character, then counting the number of vowels in the rest of the phrase." We define a vowel as being A, E, I, O or U. This is one of those problems that can just as easily be solved with traditional programming structures such as a loop - but we're asking you to use recursion for the exercise. Consider: what replaces the loop structure? When will we stop recursion? Task 2 The constant e (Euler's number) is approximated by the following sequence: 1₁ n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. 1+ 2! + ... We say that there is some value epsilon (e) such that, when the change in the approximation from one term to the next is less than said epsilon, we have reached sufficient precision. That is, when the term you're proposing to add is less than epsilon, you don't add it - you're already there. Write a recursive program to computer Euler's Number to an epsilon of 0.0000001 Check your results using an online tool like Wolfram Alpha. You will also need a helper method to compute the factorial of a number - this should also be done recursively.
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