FOR N=195, by fermat's theorem an-2 =

Q: Find one real root of g (x) = In(x*) = 0.70 between 1 and 2. How many number of iterations were…

A: Given function is gx = lnx4 = 0.70 when   lnx4 = 0.70⇒lnx4 - 0.70=0⇒ hx = lnx4 - 0.70 initial…

Q: If h(t) t" where n is a natural number, then what is h'(t)?

A: If h(t)=tn, where n is a natural number then our aim is to tell the valueof h'(t)=?

Q: Solve for r: In(x) + In(x + 2) = 3

A: Use the properties of lograthim and simplify.

Q: Estimate the value of gqΣn=2 to ∞ (1/(n2 + 4)) to within 0.1 of itsexact value

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Q: Estimate the value of to within 0.057 of its exact value. 3 - n=1 n

A: To find the value of series that comes within an accuracy of 0.057 of its exact value using the…

Q: 2) By using the iterative formula x+1= and x, 1.5, then the value of x, is O 0.3652 O 1.3652 10 of…

A: Given That :  x2+4x=10 and  xn+1=10xn+1 is the iterative formula for the given equation in [1,2] and…

Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, ....

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Q: consider this formula. z= y over x if z= 4.0 and y=6.0  express your answer to the tenths place

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Q: ZA is complementary to ZB and ZB is 8. Suppose

A: If two angles are complementary then they makes to 90°. If two angles are supplementary then they…

Q: A culture of bacteria has an initial population of 330 bacteria and doubles every 8 hours. Using the…

A: Given equation is as below: Pt = P0.2tdhere P0=330t=17d=8

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: Let floor(1) + floor(1/2) + floor(1/3) + …· + floor(1/n) = ceiling(0/1) + ceiling(1/2) +…

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Q: n is increasing, and those on w 3x + 5.

A: Introduction: The input values of a function f(x) where f(x) has minimum or maximum values are…

Q: For ƒ(x) = sin x, find ƒ"(x), ƒ″(x), ƒ‴(x), and ƒ(4)(x). What is ƒ(4n)(x) when n is a nonnegative…

A: Given  f(x)= sinx Lets take first derivative f'(x)= cos(x)f''(x)= -sin (x)f'''(x)=…

Q: solve the following P.D.E by separable method:

A: A) In this question, we need to find the solution of the partial differential equation by using the…

Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: Since a certain virus has been contained in Wakanda, researchers has proven that it will be…

A: Given that,  a certain virus has been contained in Wakanda. Researchers have found out that the…

Q: Knowing that In(1)=0, the correct second order numerical approximation of In(1.5) is ? (Use as much…

A:

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

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Q: Indicate the method you would use to prove the two A's . If no method applies, enter "none". of

A: Given ,  Here ,  Two angles are equal and one side is equal .

Q: et, a1 = 3, a2 = 4 and for n > 3,an = 2an-1 + an-2 +n², express an in terms of n. %3D

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: D If/2ty -P and 25=n(ytoc) n-T s in terms of n and P express only MS

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: A culture of bacteria has an initial population of 620 bacteria and doubles every 2 hours. Using the…

A: Initial population of bacteria was 620. It doubles every 2 hours. We have to calculate the…

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: Find x for which det(A)=0 7-x -2 A = 1- x 0. 5- x The sum of the answers is....

A: See the detailed solution below.

Q: For f(x) = x³ - x +4, compute the formula for n+1 in Newton's method. - In +4 - 3h - In 3a급-1 | In +…

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Q: Suppose x-j, for j-0, 1, 2, 3 and it is known that Find Po123(1.5). P₁1(x)=x+1, P₁2(x)=3x-1, and…

A:

Q: The average pollen count in a certain city on day x of the pollen season is  P(x) = 4x − 0.2x2 for…

A: The average pollen count in a certain city on day x of the pollen season is P(x)=4x-0.2x2…

Q: the next iterative value of the of x² - 4 = O using secant method, if the initial guess is 3 and 4

A:

Q: Then k is equal to

A: We know that integration of density function over whole range of x, is always 1. We will use this…

Q: ( Σα - xi-1) = x = x for n > 2. i=2 11 IDDLE: following "proof" th

A: Given that c, x1, x2, ..., xn, y1, y2, ..., yn are 2n+1 given numbers.

Q: Solve the equation for x In(x+ 1) + In(x – 1) = 1

A: Solve the equation for xlnx+1+lnx-1=1

Q: For #9 & 10 solve for all x in the interval [0,2x). Round to 3 decimal places only where necessary.…

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Q: solve for x if CDy=4(x-E)

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Q: (-1)" (n+ 2) 2n+1(n + 1) Compute the exact value of

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Q: (x – 2)² – In x = 0, [1,2]

A: The given equation is x-22-ln x=0 the formula for the secant method is given by…

Q: Prove that tanodo-n//2.

A:

Q: In the expansion of (2r + 1)", the coefficient of the term in x is 40n, where n e positive integers.…

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Q: A culture of bacteria has an initial population of 9700 bacteria and doubles every 2 hours. Using…

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Q: Find a positive number x such that the sum of 36x and is as small as possible.

A: We will use basic knowledge of functions, differentiation, and the second term extrema test /…

Q: 5. (8x*y® + 3x³) dx + (12x°y³ + 3xy²) dy = 0

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Q: General solution of 3 cot 0 = -V3, where n is an integer

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Q: Estimate to the nearest integer. (Examples 1 and 2) 1. V23 = 2. V197 = 3. V15.6 = Show your work. 4.…

A: Look for the square root of a perfect square near the given number. Which will be the nearest…

Q: 1. Find one real root of h (x) = 3x² – 2x = 0.5 with an error less than 5% on the interval from -1.5…

A:

Q: A culture of bacteria has an initial population of 92000 bacteria and doubles every 7 hours. Using…

A: According to question given that Pt=P0 2tA culture of bacteria has initial population =92000Double…

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: We conclude that: for every additional distress input, the brain activity increases by 0.061 units…

A: Answer:----.               Date:----6/10/2021 since slope is change in dependent variable with 1…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.