I believe I know the base case. I only need help with the successor step to...
I need to know how to proof (b) part. I didn't understand the original answer. 3. (a) Write the sum 147+10 (6n -2) using sigma notation. Solution: 2n i=1 (b) Use Mathematical Induction to prove that for all n 2 1, the above expression is equal to n(6n-1
I need some help on these two proofs... I know for the first question I am meant to prove it using the definition of a left/right limit. The second proof I am not too certain. Any help is much appreciated. Thank you! 1. Let f be a function defined on an interval I. Let a be an interior point of I Show that f is continuous at a if and only if both left limit and right limit of f...
I know a is removable, but need proof. B is discontinuous/infinite but need proof. C is infinite but need proof. They can be proved with definitions or with examples. For the following, state the set of numbers for which the function is discontinuous. Prove your claim. Classify the type of discontinuity. (25 points) x2 – 1 Vx-1 1 A. y = cot x B. y = COS X C. y = x2 – 2x – 1 3x – 2
11: I can identify the predicate being used in a proof by mathematical induction and use it to set up a framework of assumptions and conclusions for an induction proof. Below are three statements that can be proven by induction. You do not need to prove these statements! For each one clearly state the predicate involved; state what you would need to prove in the base case; clearly state the induction hypothesis in terms of the language of the proposition...
can someone help me with questions 1-5?? I need to know step by step on how to solve this math. Thank you! INTRAVENOUS CALCULATIONS CALCIO Calculate these ML/hr flow rates ranges. Express answers to the nearest whole ml/hr. (Titrate means administer.) 1. A2 g in 500 ml solution is ordered titrate at 1-2 mg/min. 2. A drug is ordered to titrate between 1 and 3 mcg/min. The solution strength is 1 mg per 250 ml. 3. The dosage range being...
Part I: Induction (90 pt.) (90 pt., 15 pt. each) Prove each of the following statements using induction, strong induction, or structural induction. For each statement, answer the following questions. a. (3 pt.) Complete the basis step of the proof. b. (3 pt.) What is the inductive hypothesis? c. (3 pt.) What do you need to show in the inductive step of the proof? d. (6 pt.) Complete the inductive step of the proof. 5. Let bo, bu, b2,... be...
Hello, I need help implementing the c++ code for successor and predecessor of a BST following the pseudocode below, thank you for your help in advance. struct treeNode { int data; treeNode *left; treeNode *right; }; treeNode* FindMin(treeNode *node) /* find the minumum node */ { while (node->left != NULL) { node = node->left; } return node; } treeNode* FindMax(treeNode *node) /* find the maximum node */ { while (node->left != NULL) { node = node->right; } return node; }...
"Proof by Mathematical Induction" is an important technique to know. We can use this technique to prove the following equation: 12+32+52 +(2n+1)2 (n+1) (2n+1) (2n+3)/3 note: n starts at 0, I.E. n 0, 1, 2, 3... To do so: (1) What is the basic step? (state the basic step, and write it using the formula above) (2) What is the inductive step? (state the inductive step, and write it using the formula above) you don't need to prove it, just...
The symbol N denotes the nonnegative integers, that is, N= {0,1,2,3,...}. The symbol R denotes the real numbers. In each of the proofs by induction in problems (2), (3), and (4), you must explicitly state and label the goal, the predicate P(n), the base case(s), the proof of the base case(s), the statement of the inductive step, and its proof. Your proofs should have English sentences connecting and justifying the formulas. As an example of the specified format, consider the...
I don't just need to know the answers but the method by which to work the problem. Any help is appreciated! PKRK sells chairs for $120 each and expects variable product costs to be $90 per unit with total fixed costs of $171,000. (Base Case) a. Determine the break-even sales units for the company. (worth 1/2 pt) What level of sales dollars should the company expect if PKRK wants to earn an operating profit of $85,000? (worth 1/2 pt) b....