T(n) = T(n – 1) + 1 T(1) = 1 %3D O o (n?) O(log n) O O(n)

Q: | log x? dx A. log x? +x + C C. x log x? – 1 + C B. x log x? – 2x + C D. x log x² + x + C -

A: The given integral is ∫logx2dx. Use the identity logab=bloga. The integral will be…

Q: Selberg identity For n 21 we have A(n) log n + ΣΑ(d) (%) Σμα din

A:

Q: 5. Solve for x using log properties: log3 (x) + log3(2x – 3) = 2 |

A: Consider the given logarithmic equation, log3x+log32x-3=2 use the logarithmic property,…

Q: Sales (in thousands of units) of a new product are approximated by the function S(t)=60+20 log 3…

A:

Q: Find the value of x satisfying log,, (2×+x– 41)=x (1 – log1,5).

A: It is given that, log10(2x+x-41)=x(1-log105)   Here logarithmic properties are going to be useful to…

Q: *dx 2x- In Ixl+ C 1 x² - In Ixl+ C | 2x 4 In Ixl+ C x² – 4 In Ix| + C O A В E None of the Above

A:

Q: Let f(n) = ((3.6) n + 14 log7 (5n³ - 19n²)) x 14√/2n +6. Which of the following is true? (Select…

A: Let's analyze the given function again with the updated information:Given function: f(n) = ((3.6)n +…

Q: dx Evaluate: √(x+1) log(x+1) A In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C C In[log(x+1)] + C In 10…

A: Evaluate ∫dxx+1logx+1

Q: Given that the runtime efficiency is: f(n) = 10 log(n) + 5 (log(n))³+ 7n + 3n²+ 6n³ Which statement…

A: Answer:- Option(d):- f(n) is O(n3)

Q: Find the Big-O estimation of f(n) = n¹(n − 2)² + nª log(n³ + 6n)

A:

Q: Find the inverse of the function. Ax) = log1/13*

A: Let the function is f(x)=y=log1/13 x Let f(x) be the function. A function g(x) is said to be inverse…

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: dx The is equal to (x + 1)log(x + 1) -In10· log?(x + 1) + C O 히og2(x+ 1) + C 1 © niohlog(x+ 1)] +c…

A: ∫1x+1logx+1dx To check: Which of the options is correct out of a,b,c,d,e.

Q: Sales (in thousands of units) of a new product are approximated by the function S(t) = 200 + 45log 3…

A:

Q: Solve the following d. In 3- Inx - In (x + 5) = 0 e. Log4 (x+ 2)- log4 (x - 1) = 1 f. Log2 (x-1) –…

A: The detailed solution is as follows below:

Q: Let f(x) = x and g(x) = log₁ x. Find [f(x) • g(x) dx (A B d dx -[f(x) • g(x)] d dx =[f(x) • g(x)] =…

A: Given; f(x)=x and g(x)=log5x.

Q: Give as good a big - O estimate as possible for the following function: f(n)= (n logn + n²)(n³ + 2)…

A: We find big-O estimate of the given function.

Q: hematics “ Give a big-o estimate for the following functions where n is a positive integer.

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Q1: What is the least integer n such that f(x) is 0(x") for: a) f(x) = 123x² + x³ log x b) f(x) =…

A:

Q: (a) Show that the function f : N→Z+ defined by f(n) = n! is not O(n). (b) The function g : R+ + R+…

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Q: Show Recurrence that the solution to T (n) = T (2n/3) + 1 is Θ( log2 n)

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Q: Show that n log n is Θ(log n!)

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Q: Let n be a positive integer and f(n) = 2n10 - n51- 53. Then f(n) is None of these

A:

Q: Given this function: f(n) { k = 0 for i = 1 to n { for j = 1 to n { k:= k + 1 } } return k } Which…

A: Calculate the operations in for loops

Q: 17. Solve log3 (5z +1) > log;(3z +1)

A:

Q: 4. We have seen in lectures that the differentiation of a function given by valid power series…

A: If limn→∞ |an+1an|=Lwhere L is a positive real number or L=0 or L=∞, then the power series…

Q: Let n be a positive integer and f(n) = -3n52 +7 n51- 51. Then f(n) is O(n51) equal to the above…

A: Consider the given function, fn=-3n52+7n51-51 where, n be a positive integer.

Q: Prove or Disprove: n 8 + 3 n 7.9 log n − n4  = Θ( n 8 ).

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.