(a) Suppose that f is a polynomial of degree 3 or more. Explain, in your own...

(a) Suppose that f is a polynomial of degree 3 or more. Explain, in your own words, how you would

use real zeros of f to determine the open intervals over which f(x) > 0 or f(x) < 0. Be brief

and precise. In particular, you need to tell how and where the sign of f changes.

(d) Rewrite the expression (cos x)2x in terms of natural base e.

4. Let f(x) = x2 + 5. Find lim_h-0 f(3+h) - f(3)/h

Expert Solution

milcah answered 2 years ago

If f is a polynomial of degree 3 or more how would you use real zeros...

If f is a polynomial of degree 3 or more how would you use real zeros of f to determine the open intervals over which f(x) > 0 or f(x) < 0. How and where does the sign of f change.

Suppose f is a degree n polynomial where f(a1) = b1, f(a2) = b2, · ·...

Suppose f is a degree n polynomial where f(a1) = b1, f(a2) = b2, · · · f(an+1) = bn+1 where a1, a2, · · · an+1 are n + 1 distinct values. We will define a new polynomial g(x) = b1(x − a2)(x − a3)· · ·(x − an+1) / (a1 − a2)(a1 − a3)· · ·(a1 − an+1) + b2(x − a1)(x − a3)(x − a4)· · ·(x − an+1) / (a2 − a1)(a2 − a3)(a2 − a4)·...

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given...

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −5, 1, 2; f(3) = 48 Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −3, −2, 0; f(−4) = 24 Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −2i, 2i, 5; f(1) = 40 Find the zeros of f(x), and state the multiplicity of each zero. (Order your...

Find the Taylor polynomial of degree 2 centered at a = 1 for the function f(x)...

Find the Taylor polynomial of degree 2 centered at a = 1 for the function f(x) = e^(2x) . Use Taylor’s Inequality to estimate the accuracy of the approximation e^(2x) ≈ T2(x) when 0.7 ≤ x ≤ 1.3

Let f be an irreducible polynomial of degree n over K, and let Σ be the...

Let f be an irreducible polynomial of degree n over K, and let Σ be the splitting field for f over K. Show that [Σ : K] divides n!.

Task 3: a) A second-degree polynomial in x is given by the expression = + +...

Task 3: a) A second-degree polynomial in x is given by the expression = + + , where a, b, and c are known numbers and a is not equal to 0. Write a C function named polyTwo (a,b,c,x) that computes and returns the value of a second-degree polynomial for any passed values of a, b, c, and x. b) Include the function written in part a in a working program. Make sure your function is called from main() and...

Given: Polynomial P(x) of degree 6 Given: x=3 is a zero for the Polynomial above List...

Given: Polynomial P(x) of degree 6 Given: x=3 is a zero for the Polynomial above List all combinations of real and complex zeros, but do not consider multiplicity for the zeros.

compute the 2-degree polynomial approximation of f(x)= 3x-e^x^2

consider f(x) = ln(x) use polynomial degree of 5!!! a) Approximate f(0.9) and f(1.1) b) Use...

consider f(x) = ln(x) use polynomial degree of 5!!! a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an error formula for Taylor polynomial. Give error bounds for each of the two approximations in (a). Which of the two approximations in part (a) is closer to correct value? c) Compare an actual error in each case with error bound in part (b).

Find polynomial of degree at most 1 best approximates function f(x) = ex in the sense...

Find polynomial of degree at most 1 best approximates function f(x) = ex in the sense of uniform approximation on [0,1]. give the error of approximation of the function f with this polynomial.

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