f(x) = e^-1/x^2 show that there is no positive number M such that each natural no n, |f^n(x)|< M^n

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: What happens in Newton’s Method if your initial guess happens to be a local min or max of f ?

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Q: Use integration by parts to verify the reduction formula.

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Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: Express in exact form: In(x² + 1)dx

A:

Q: Use finite approximations to estimate the under the graph of the function f(x) = 4 – x² between x =…

A: Here given that a function and find lower sum with four rectangles of equal width. Here i attached…

Q: tion, what is the longest time within whic at the predator will have to spend more t

A: It is found that the time (in minutes) required by predator to find a prey is a random variable that…

Q: Prove 9 coshx – 5 sinhx = 15

A: This is hyperbolic function equation so we want to find x value by thi equation so. firstly, we…

Q: Compute for a real root of 2 cos x – sin vx = i accurate to 4 significant figures using Fixed-Point…

A: 2cosx3-sinx=14  compute for a real root of equation using fixed point iteration method with an…

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: 2- Find the positive root of f(x) = xe"- cos(x) with an error tolerance =0.005% by using the secant…

A: Using a graph, it can be found out whether a function has solutions if the graph cuts the x-axis at…

Q: 1. Determine where f(x) = arcsin (x² – 2x) is increasing. %3D

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: 2. Compute for a real root of sin -x 0 using three iterations of Fixed- Point Iteration Method with…

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Q: 2. Compute for a real root of sin va - x = 0 using three iterations of Fixed-Point Iteration Method…

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Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: Use Fixed-Point Iteration Method to obtain a real root of x^3-5x+1=0 with x₀=0 until absolute error

A: Solutions

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: how do we identify the minimum and maximum value of the graph of a function at a given intetval?

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Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x) =…

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Q: у" - In x

A: Given: y''=lnx

Q: logtan nx(2+ 4 cos nx) 2

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Q: 3 11 lim *+3 9. x→2 2х - 4

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Q: Compute for a real root of 2 cos √x - sin √x = 4 accurate to 4 significant figures using Fixed-Point…

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Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Assuming an initial bracket of (-0.5, 0), what is the approximate value of the root of f(x) = 3x +…

A: The false position method can be used to calculate the root of the function. The formula for the…

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x) =…

A:

Q: . Compute for a real root of 2 cos VI – sin Va = + accurate to 4 significant figures using…

A: Given equation is 2cos x3 - sinx =14 And, initial guess:- x0 =π Also, 2cos x3 - sinx =14⇒ x  = cos-1…

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x)…

A: Let's find.

Q: What is the second iterative value of the root f(x) = x2 - 3. with the initial bracket [1, 2] using…

A: To find The second iterative value of the root of f(x) using the bisection method.

Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: (textbook, section 0.4, exercise 5) Evaluate the quantity V16x+- x² - 4x wherex = 8.0, correct to at…

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Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: This is exercise 26 of Section 7.5 page 460. Find the integral æ* sin(æ²) dx-

A: Answer is given in the picture

Q: if X #0 メ=ロ Frnd continuous

A: given the function fx=xx if x≠00   if x=0 we know that x=x if x&gt;0x=-x if x&lt;0 therefore,…

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

A:

Q: How many iterations are needed to obtain the root of f(x) = 3x + cos2x if the bracket is (-0.5, 0)…

A: False position or Regula Falsi method uses the formula below to perform the iterations.…

Q: Find all critical numbers of f(x)=3x+sin(3x)

A: Given,   f(x)=3x+sin(3x) We have to find all the critical numbers.

Q: Determine the root of f(x)=xr – e* using fixed point iteration and false position method with…

A: Given function is fx=x-e-x The initial value is given as x0=3 In the fixed point iteration process…

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

A:

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

A:

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.