a? - 1 x² + 2x+- at -5' x+2 ;x>0 Let f(x) = { Find all possible real values of a such that f(x) possesses the smallest value at x = 0.

Q: What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

Q: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

Q: 4. Determine the root of F(x) = 7 sin(x)e-x – 1 using secant method with 3 iterations glven Xi-1 =…

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Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: Find the domain and all critical points in the domain y=ln(x-5)

A: Domain: (5,∞),{x|x>5}

Q: Find the Absolute Extremum of F(x)=2sinx-cos2x over [0,2pi]

A: Consider the following:  Differentiate the function and find critical point:…

Q: 11. Use the Mean Value theorem to show that f(x) = 2x sinh (æ – 1) + 2" – x has a critical number…

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Q: 4. 1. Let f(x) = (sinx)*tan(1 – x)e30x. Find the maximum of f(x) in [0,1] and ɛ = 0.05. (by handly…

A: Given: fx=sinx6tan1-xe30x. We have to find the maximum of fx in 0,1.

Q: 38 Find the critical numbers of the function. 25. f(x) = x³ + 3x² – 24x %3D -

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

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Q: 17. Why doesn't the definite integral 1-x² dx make sense? (Hint: Think about domains.)

A: To find: The reason why the definite integral ∫231-x2dx does not make sense. Explanation: Substitute…

Q: 7. Use the Intermediate Value Theorem to find an interval of length 1/2 in which the equation In r =…

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Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: Find the critical points of f (x) = 2 cos 3x + 3 cos 2x in [0, 2π]. Check your answer against a…

A: Given: f(x)=2 cos(3x)+3 cos(2x), 0, 2π

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: Apply the secant method to solve f(x) = e** In x² – x = 0. Discuss the procedure for dealing with…

A: We are given the following function.  f(x)=ex2lnx2-x=0. We have to solve by the secant method. Note…

Q: Consider a function f with domain {x|x # 0} and the following derivatives: f'(x) = bx-1 and f"(x) =…

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Q: 3. Use Rolle's Theorem to show that the function f (x) = x² sin(x) – x sin(x) has a critical point…

A: For y = f(x). Let f(x) is continuous at every point of the closed interval [a, b] and differentiable…

Q: 73 9x +4 then f(x) has a local maximum at the point 3 Use second derivative test, If f(x) %3D - O…

A: Topic:- application of derivatives

Q: 5. Find the exact absolute maximum and absolute minimum values for f(x) cos(x) + sin (x) on the…

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Q: 4. 1. Let f (x) = (sinx)ʻtan(1 – x)e30x. Find the maximum of f(x) in [0,1] and & = 0.05. (by handly…

A: We will use Newton's method of optimization to find the maximum value of f(x)

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: 5. Find the absolute minimum and absolute maximum values of f(x)= 2cosx +sin2x on the interval 2 N

A: Consider the given function,To find the absolute minimum and maximum values of the given function,…

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the x-coordinates of all local minima and…

A: Given:f(x)= (3x^2)ln(x) , x>0

Q: 12 11. Find the critical points of f(x) 4x? ). Then use the Second Derivative Test to determine if…

A: Here, we need to find the critical points of f(x)=x127x3-4x2. Now, f'(x)=6x2x-10xx and…

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Consider the given function as y=xlnx

Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

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Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: find the absolute maximum and minimumvalues of each function on the given interval. y = 10x(2 - ln…

A: Given function is:                              y=10x(2-ln x) over (0, 2e)   To determine:…

Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: f(x)= X-I x=1 √x-1 X = 1 1123 -s continuous at x = 1?

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Q: Consider the function f(x) = x – 3 ln(x) on the interval 3 The absolute maximum value is and this…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. ln(x^2+3x+8) in…

A: Given:

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Discuss the extreme-value behavior of the function ƒ(x) = x sin (1/x), x ≠ 0. How many critical…

A: Given fx=xsin1x,x≠0

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 Where is the function increasing and decreasing in…

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Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: At which points does f(x) = 2 sin x - cos 2x have an absolute maximum value and what is the maximum…

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Q: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

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Q: x = -1 is a critical number for g(x) = xª +x³ +x - 1. But the second derivative test fails for x =…

A: Explanation of the answer is as follows

Q: 1. Find all the local and global extrema of the function f (x) = sin(x) – x [-27, 27]. Clearly…

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Q: Find the critical numbers of the function  f(x) = 2cos x + sin 2  x

A: Since, we have been given that f(x)= 2 cos(x) +sin2 (x) -(i)Our Aim is to find the critical numbers…

Q: The approximation of the root x* of the function f(x) = ln(x + 1) - x + 3 accurate to within 10-2…

A: Introduction: Another recursive technique for approximating the polynomials' roots is the secant…

Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

A: