3. Invent two interesting and original positive integers a and b. Let f(x) = ax +3. (a) (b) What is f(10)? Find a number z such that f (x) = b. Calendar OCT tv

Q: 8. The domain of - consists of numbers x for which g(x)_0 that are in the domains of both – and,

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

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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: Give an expression for f(x) of degree 3 with roots z = -4 and r = -2, where the root at r = -2 has…

A: Zeroes are x=-4 and x=-2and x=-2 has multiplicity 2

Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: 67 Find the lowest order polynomial which approximates the function f(a)- (-x in the range 0 sxs1,…

A: We will use basic knowledge of numerical analysis to answer this question.

Q: 7. Suppose f(x) = x³ – 27x + 1. Prove that f has exactly one root (zero) in the interval [0, 2].

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Q: (a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7…

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Q: 2. Estimate the root of f(x) = In x; ɛEs = 0.1%. Start the computation with values of xl = xi-1 =…

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Q: If f(x) has odd degree and negative leading coefficient, as x goes to -∞, then f(x) would go to

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Q: Is f(x)= In (x^2)+1 odd, even, or neither? Show all the work

A: A function is said to be even if, f(x)=f(-x) and a function is said to be odd if, f(x)=-f(-x). If…

Q: 7. The fourth-degree polynomial f(x) = 230x* + 18x + 9x? – 221x -9 has two real zeros, one in [-1,0]…

A: As per the guideline, I am doing the 1st method only. Kindly repost the others separately.   Secant…

Q: 1. prove that if x is real number then ,[2x] =[x] +[x +1/2] when [x] denote the greatest integer…

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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: Determine whether Rolle's Theorem can be applied to 22 –1 f (x) on the closed interval –1, 1. If…

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Q: f is increasing on (a, b) of for all x1, x2 in (a, b) when x1 less than x2,f(x1) less than f(x2).

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Q: Show that when x increases from 1 to 1.25 and when it increases from 2.75 to 3, the value k of grows…

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Q: 9. Use the given graph of f (x) x2 to find a number 8 such that %3D if |x – 1| < 8 then |x2 – 1| <;…

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Q: 1. Let f:R R be defined by {1 if x rational number, 12 if x irrational number f(x) = Show that f is…

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Q: 4cos20 + 2/3 = 0 on the interval[0, 3t]

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Q: List all the polynomials of degree 2 in Z2[x]. Which of these areequal as functions from Z2 to Z2?

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Q: 3. Use the Intermediate Value Theorem to show that f(a) = a2-3x +1 has at least one real zero…

A: According to intermediate value theorem, if f(x) is a continuous function whose domains contains the…

Q: 14) Use the Intermediate Value Theorem to show that the po zero in the given interval. g(x) = 2x³ –…

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Q: 5. For z=x2siny show that 332 332 = дудхду дугдх

A: Topic = Derivative

Q: 3. For f (x) = 2x³ + 4x² + 3x – 7, prove that there exist a number k such that f(k) = 20.

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Q: Show that f(x) = x5 +2x4-6x3+2x-3 has a solution between 1 and 2. Use the intermediate Value…

A: The equation given to us is  f(x) = x5 +2x4-6x3+2x-3

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: 5.5 (a) Determine the roots of f(x) = -12 – 21x + 18x2 – 2.75x3 graphically. In addition, determine…

A: Given: f(x)=-12-21x+18x2-2.75x3 To determine: Root of given function by a) graphing method. b)…

Q: What is the smallest integer a where f(x)=2x is always greater than g(x)=x2 for all x>a?

A: Given  : f(x) = 2x is always greater than g(x)=x2 for all x &gt; a  Implise that :  2x &gt; x2

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: Since x^4+x-8 is a polynomial it is continuous.Answer: f(x)=x^4+x-8 is continuous on the closed…

Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: 5. Find all pairs (m, n) of positive integers such that y(y(nm)) = n, where p is Euler's totient…

A:

Q: For the pairs of integers a=13, b=32, find the gcd g and integers x and y satisfying g=ax+by. Attach…

A: Given that, the pair of integersa=13,b=32 The equation is: g=ax+by where g is the gcd.

Q: find an integer n such that f(x)= 0 for some x between n and n+1. f(x) = x^3 - x + 3

A: Given:The function f(x) = x3−x+3.Known fact:Newton Rphson's method.It is an iterative process to…

Q: - Give the domain for k(a) in interval notation. x2 + 3x +2

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Q: (It v5)" (1 Vsy (b) Prove that f. for all integers n> 1.

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Q: Prove that the function f : R → R is not continuous at xo = f(x) = { 2 +1 r40 if x E Q if x 4 Q…

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Q: Prove: for n > 1, F; – Fn+1 Fn-1 = (-1)".

A: F_n are the Fibonacci numbers which are defined by F_0=1,F_1=1 and F_n = F_{n-1}+F_{n-2} for…

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: 5.5 (a) Determine the roots of f(x)=-12 – 21x + 18x2 – 2.75x³ graphically. In addition, determine…

A: The root of a function is the point on the graph which touches the x-axis. To find the root using…

Q: 4) Consider the function fex)= Slx-s] Evaluate 7-4 for any There is no solution to the equati on…

A: Given: fx=5x-5 so, f7-f47-4=57-5-54-57-4=52-13=513=53

Q: 2) Find the 3€ Tayler polynomial P,(x) fix) = Sinx at X= -½. 3) Using B,(x) from 2), estimake sin…

A: The formula for taylor series is     where f (k) (a)  is kth derivative of f at given point a.

Q: Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of…

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Q: -21 -42 -63 -84 -105 -126- -147 -168- -189- -210 For the above quartic polynomial f( x ) = 1.5a –…

A: To find the interval on which f(x) is concave down.

Q: 7. Determine whether the funcion is even, odd, or neither: f(x) = 1+x2

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Q: 6. Find the third degree Maclaurin polynomial for f(x) = cot-(x) and use this to approximate…

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Q: 4. Suppose that f(2) = 16 and that f'(x) > – 3 for all x in the interval [2,7]. Determine the…

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Q: True or False The domain of 1f # g2 1x2 consists of thenumbers x that are in the domains of both f…

A: The domain of (f·g)(x) consists of the numbers x that are in the domains of both f and g

Q: 3. Without referring to its graph, clearily explain why P(x) =4--6x +4 has an output of Vi on the…

A: 3. Given function is Px=4x3-x2-6x+4