{x0.5,x-1/3}

Q: let g(x)=     (2x2++2x-24) / (x3-16x) the holes and vertical asymptote(s) for this function exist…

A: let g(x)=     (2x2+2x-24) / (x3-16x)Let's factrorise the numerator and denominator.Numerator =…

Q: Consider the following. g(x) - x* - 2x2 + 7 Find g'(x). g'(x) = Find the critical numbers of g(x).…

A: Topic - application of derivatives

Q: 3. It is easy to observe that root of f(r) = r² – 8 lies in the interval [2, 3]. Use Bisection…

A: Given function is fx=x2-8. It's root lies in interval 2,3 Since f2=4-8=-4<0 and  f3=9-8=1>0…

Q: 8. Construct a natural cubic spline that interpolates the function f(x) = 1/(1+ x²) at x = -2, –…

A: Let the cubic spline polynomial of f(x) be H(x). Then Hx=fa+fa,ax-a+fa,a,bx-a2+fa,a,bx-a2x-b…

Q: The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01, and 0.005. In contrast, the χ2-table…

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Q: (a) What is the Taylor polynomial of degree 2 for g near 7? P2(x):

A: Taylor series of any function with center x=a is…

Q: Suppose X - X(3). Find k such that P(X > k) = 0.01. Round your answer to 3 decimals. k :

A: It is needed to find the value of k, such that, P(X > k) = 0.01.

Q: 1. Given the function f (x) = 5x2 - x - 2, Determine the approximate root of the %3D function and…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the root of x4-x-10 = 0 approximately upto 5 iterations using Bisection Method. Let a = 1.5 and…

A: The root of x4-x-10=0 between a=1.5 and b=2

Q: Consider the following. g(x) = x4 – 2x2 + 6 Find g'(x). 9'(x) = Find the critical numbers of g(x).…

A: The given function is g(x) = x4 − 2x2+ 6

Q: Which of the following is a critical number of f(x)= 4. 2x %3D

A: The given functIon is: f(x)=14x2-2x

Q: Consider the following. f(x) = x4 - 9x2 g(x) = x2 - 9 %3D (a) Use a graphing utility to graph the…

A: A)

Q: 1. Using excel program, create an algorithm that will solve the root of the function using Regula…

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Q: (b) Expand and simplify in ascending powers of x as far as the term in x" 1+3x

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Q: If f(1) = 2 and 3 <f'(x)<5, what is the largest f(4) can be? Be sure to fully justify your work. In…

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Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

A: Given: ∫abf(x) dx and the function f(x), where the interval of integration a, b is divided into n=3…

Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

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Q: Consider the following function: f (x) = x* + 2x + 81 + 5x Employ Golden-section to find the maximum…

A: Determine two intermediate points  x1 and x2 such that  x1=xl+dx2=xu-dd = 5-12(xu-xl) here  xl=-2…

Q: ased on its degree and leading 3. G(x) = -2x+ 3x2-x+ 1. %3D Write your description here.

A: As per our guidelines we are supposed to answer only one question please post another question as…

Q: 6) Show that the function f:Z → N given by 2n +1, n20 f(x) = -2n, n<0. is 1-1 and onto. I

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Q: 4. Find an upper and a lower bound for the set E= x +1 : -1 < x2 +1

A: Given: E=x+1x2+1:-1&lt;x≤2

Q: Let f₁(x) = x² and f₂(x) = x³. Complete the Wronskian for these functions. |x² w(x², x5)= 2x

A: Wronskian is a deteminant which is test for proving whether solutions are linearly independent or…

Q: a PDE from the following- @u =f() Form メソ

A: We eliminate the arbitrary function f from the given equation to form the required partial…

Q: Q1) Determine the halve range odd expansion of the function whose definition is: 0≤x≤1 f(x) = - {...…

A:

Q: Which of the following best describes the transformation of y = -5Vx from f(x) = Vx? F. horizontal…

A: A vertical stretch is given by the equation y=bf(x).  If b&gt;1, the graph stretches with respect to…

Q: Show that the generating function for compositions into an even number of parts, each of which is…

A:

Q: Use the Fibonacci algorithm to find the minimum of 1 2(x- 1) log r- (x – 1)2 f(r) = I+1 which is…

A: From the given information. The function for which the minimum has to be calculated is as follows.

Q: Find the domain of the function. k(x) = In |x|

A: The domain of a function, f(x)  is the set of input values of x for which f(x) is real and defined.

Q: Find the Wronskian for the set of functions {e5x, e-5x}

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Q: 1) Find the root of f(x) = x3 + x - 1 = 0 , lying in the interval (0,1) using Bisection method up to…

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Q: Consider the following.  f(x)= Square root of 49-x2 a) Find the critical numbers. b) Find the…

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Q: Consider the minimization of the function f(x1,x2)=4x21+3x22−5x1x2−8x1 with starting point X0=[00]…

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Q: T(n)= 3T(n-1)+ 4 base case: n = = 0

A: We will first find characteristic equation then its roots and then we find the general solution of…

Q: 5. Consider the following function: f(x1, x2) = -(x1 – 2)? – x1 – x3. %3D (a) Use the steepest…

A: Given that  fx1,x2=-x1-22-x1-x22 Solution of part (a): We want to maximize f by steepest descent…

Q: Show that lGl =20 , so G is not simple

A:

Q: - 4x³| [x-2x] ,1s x<2 Os x<1 Let f(x) = Then discuss the differentiability of f(x) in (0,2) Here []…

A: Given that: f(x)=|1-4x2| ,    0≤x&lt;1[x2-2x] ,      1≤x&lt;2

Q: What is the run-time complexity of the of the recursively defined Closed form function T(n)=3T(n-1)…

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Q: Find the area of the following z-values and draw its graph. From and to the left of z= 2.0 Please…

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Q: 5. T(n)= 3T (%) +2n base case: n = 1

A: Solution:

Q: 1. Evaluate the following Improper Integral. Does the limit converge? Why or why not? [Apply the…

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Q: 10. Find all of the discontinuities that exist for g(x) = 2*+3x-4 Show any work required to %3D x+1…

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Q: 2: find the function H by Cayley-Hamilton-Sylvester -2i

A: Here we will find out H-1

Q: Find critical number of g(x) = x^2 - 8x +9

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Q: What is the expansion of f (x) = 1/1-x

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Q: Find V2 to the correct six decimal places using Newton's method. (Hint: Use the equation f(x) = x³ –…

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Q: 8. Find a closed form representation for the function defined recursively by f(1) = 10 and…

A: Definition: Here is the master's theorem for recurrence relation is follows, Tn=aTnb+cnk, T1=c1…

Q: 5. Find the domain of the function: y = In () x-4

A: y=lnx-1x-4

Q: Given the function h(x) = In(-x² + lx) with k a real number and k > 1. If h'(x) - -2x+k lx - x? %3D…

A: