Wich of te following is not a factor of f(x)=x^3+2x+3 in Z5[x] a. x+1 b. x+2 c. x+3

Q: 6(x² + 3) ((x – 3)(x + 3))³ 1 -2x f(x) = f (2) = f (x) = (x – 3)(x + 3) ((г — 3)(х + 3))?

A: Since, the numerator is a constant 1, so, the graph has only one horizontal asymptote which is the…

Q: Use Muller's method to determine the po a. f(x) = x³ + x² - 4x4 b. f(x) = x³ -0.5x² + 4x - 2 c. f(x)…

A: Here, in the question we are given three set of equations for which we have to find the real root…

Q: Find the horizontal asymptote of f (x) = 8-822-240z 3z-3z2 60z Section 3.4 Oy = Oy = 4 Oy= Oy= 0 Oy…

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Q: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

A: Given: The function is  f(x)=4-x3,  -2≤x≤1   To determine: The absolute extremum of the function…

Q: 4) Find the absolute maximum and absolute minimum values of f on the given interval. (a)f(x) = 3x² –…

A: Find the absolute maximum and absolute minimum values of fa) f(x)=3x2-12x+5 , 0,3 b) fx=x-lnx , 12,2…

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: Which of the following is a polynomial f(x) of degree 3 with real coefficients which

A:

Q: 5. Find all the zeroes of the function f(x) = - 0.5x + 2.5 x+ 4.5 using False Position Method…

A:

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: Find a formula for f-(x) and (f-1)'(æ) if ƒ(x) = -V5 – x f-' (x) = (5-1)'(x) =

A:

Q: Find the absolute extreme of f(x)=x^3-12x on the closed interval [0,4]

A: for finding critical points take f'(x) = 0 then find the function value at the critical points and…

Q: Find all critical values for f(æ) = (x – 4)°(æ – 5)*. %3D - The critical values occur at X = commas)

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Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

A:

Q: Example 2: Using the False Position method, find an approximated root of the function: f(x) = x² –…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

A:

Q: Consider the following equation. 3x4 − 8x3 + 8 = 0, [2, 3] (a) Explain how we know that the given…

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

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: Find the critical points of the following function. Assume a is a nonzero constant. ƒ(x) = 3x2 - 4x…

A: Given function  fx=3x2-4x+2 To find the critical points differentiate the given function and equate…

Q: ,for x 1 Discuss the contuniuty of f andf'.

A:

Q: 2x 10) Consider f(x) = 3-4 on the interval [2,6. Find the maximum and minimum values of f(x on the…

A: The given function is,

Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

A:

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

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Q: Consider the following equation. 3x4 8x3 + 2 = 0, [2, 3] (a) Explain how we know that the given…

A:

Q: sketch the following rational functions by determining all critical values. h(x)=x2-2x-8/x2-9

A: To evaluate the critical points of the rational function h(x) = 0 we must solve the equation h'(x) =…

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: The interval where  f(x) = )=(√x+2) / x2 - 2x - 8 is continuous is ?

A:

Q: 6. Find the absolute extrema of the function f (x) = 7x² + 1 on the closed interval [-1,2].

A: We need to check value of f(x) on critical points and boundary values of interval to find absolute…

Q: 6. Obtain the TSE of f(x)=2x-² in powers of (x-1).

A: Solution is here

Q: Find the vertical and horizontal asymptote(s) of f(x).

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a…

Q: 7. Let f(x) = x³ + 3x – 2. a In view of the fact that f(0) = -2 and f(1) = 2, why would you expect…

A: This is odd degree polynomial so it have range of a real number and.  Imaginary roots comes in .…

Q: Verify the assertion made in Example 2.

A:

Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

A: A function is a relation from a set of inputs to a set of possible outputs where each input is…

Q: Find the are under the graph of f(x) = 4-x2  on the interval (-2,1)

A: Given, f(x) =4-x2  we have to find the area under the curve on the interval (-2,1)

Q: 7. Evaluate a root using Muller's method from the function. Terminate if Es < 0.0055% f(x) = 0.5x4…

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Q: (1) Find and classify the extreme values of f(x) =6x* -4x over the interval [-2,2].

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Find the coefficient of x25 in the generating function (x+ x2+ x3 + x* + x5+ x®) 4 (x²+ x³ + x*+..a…

A: Given function is, x+x2+x3+x4+x5+x64x2+x3+x4+...3 Now, we can write the given equation as,…

Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: sketch the following rational functions by determining all critical values. f(x)=3x2-x3/x2-9

A: The given function is f(x) = 3x2-x3x2-9,This function is not defined at x = -3, x = 3.We try and…

Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

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Q: 11. Determine the absolute extreme values of f(x) = xe-/2 = xel-/2 on the interval [0, 5].

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

A: