13. When is a polynomial f(x) of at most the order of a polynomial g(x) as x→∞? Give reasons for your answer.

Q: Suppose that f(x) is a polynomial of degree 3. Show that f(x) is its own clamped cubic spline, but…

A: The nth degree polynomial can be represented as Pn=a0+a1x+a2x2+…anxn. It is known that ddxxn=nxn-1.

Q: Find the linearization L(x) of the function at a. 9 f(x) = a = 3 - L(x) =

A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3

Q: Discuss separability of the polynomial <³ +2ײ+3 3 over Jh5

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Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: The function is given as fx=x2e-x

Q: 4х — 5 8. Consider the rational function defined by y = 2(х + 1)?(х — 3)" Make a table of values to…

A: The solution is given as follows

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: Find the Taylor polynomial po for f(x) = at z = 1.

A:

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: 4х+7 (ii) If f(x)={ 1<x<2 determine whether the function f(x) is continuous 14x² -1 2<x<4 throughout…

A: Continuity of the function

Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

A:

Q: 3. Let f(x) = ax°+bx2 + cx+d be any polynomial of degree 3 or less. Show by direct computation tha…

A:

Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

A:

Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: Given function is: fx=e4x We have to find f14.

Q: Suppose that ?(?) is differentiable on an interval centered at ? = ? and ?(?) = ?0 +?1(? − ?) + ⋯ +…

A: Given question:   Suppose that ?(?) is differentiable on an interval centered at ? = ? and ?(?) = ?0…

Q: 4. Why is f'(x) approximated well by the difference quotient when Ax is very small?

A: Derivative of function f by definition is: f'x=lim∆x→0fx+∆x-fx∆x This is the difference quotient…

Q: 2. Will the limit of all polynomial functions / (x) as x approaches a be always equal to the value…

A: Find your answer below

Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

A:

Q: Suppose that the function f(x)  is continuous everywhere. Suppose further that the points (Xj, Yj),…

A:

Q: 1) Let f(x) = e2* Find 3rd Maclaurin Polynomial for f(x)

A: Given f(x)=e2x To find the third order maclaurins polynomial

Q: 4. The graph of the polynomial function f below. If g(x)=f(x+5)-1, what are the roots of g(x)?

A: Given ,  The graph of the polynomial function f  If g(x) = f(x + 5) - 1  We have to find the roots…

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: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

A:

Q: 15.B. Show that a polynomial function f, given by f(x) anx" + an-1x"¬1 +... + a1x + ao, x€ R, is…

A:

Q: I Example 6.10. Assuming that the following values of y belong to a polynomial of degree 4, compute…

A:

Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: Let Q(x) be any polynomial of degree ≤ n with real coefficients and let M be the maximum of Q(x)| on…

A:

Q: Let f (x) be a function whose Taylor polynomial of degree 4 about x 2 is given by P(x) = 2 + 3(x 2)2…

A:

Q: Let p (x) be a polynomial. Then limn->o∞ p(n) O Cannot be determined

A: Topic:- calculus

Q: 5. Show that the function f (x) has roots between (0,2) x + 2x – 3 f(x) = %3D x – 1

A: Given that: f(x)=x2+2x-3x-1

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: 3. Use Lagrange interpolating polynomial of degree 4 to estimate f(1.9). 0.5 1.2 1.7 2.1 3.0 f(x) 1…

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Q: 1. Describe how to find the limit of a polynomial function p(x) as x approaches c.

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Q: estimate the value of x correspond to f(x) = 1.6 Using cubic interpolating polynomial together with…

A: Given data is x 1 2 3 4 f(x) 3.6 1.8 1.2 0.9 The value of x corresponding to f(x) = 1.6…

Q: what should n be if f(x) = Xn defineof a polynomial function?

A:

Q: Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Given,  f(x)=ex

Q: Q2.15 Let gcx) = 4x4 (9x) is the a for 2≤x≤4. which result of using Taylors inequality [₂(x) is…

A:

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

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Q: c) Prove that there cannot exist two different polynomials q,r E K[x], both of degree less than n,…

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Q: 14. What do the conclusions we drew in Section 2.8 about the limits of rational functions tell us…

A: Note that higher degree polynomials grow at a rate higher than the polynomials of less degree.

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: 16) what are the vertical asymptote(s) of f(x) = x+5x-6, %3D x² -1

A:

Q: 22. The function In x grows slower than any polynomial Show that In x grows slower as x → oo than…

A:

Q: There is at most one polynomial of degree less than or equal to n which interpolates f(x) at (n+1)…

A: By using interpolation theory, we need to check which of the given options are true.

Q: is a polynomial O has repeated roots at x = 0 O has a slope equal to zero at x = 0 O is always…

A:

Q: 18. Given the polynomial irrational roots. f(x)=2x²-x²-5 . use linear interpolation to approximate…

A: Given: The polynomial is fx=2x3-x2-5. To find: The roots of the given polynomial.

Q: How many different numbers of critical points can a cubic polynomial have? Give an explic…

A: In this question we will use basic of calculus i.e concept of critical points. We will assume a…

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

A: