To say that |r – 7| < 2 is the same as saying æ is in the closed interval [A, B] where A is: and where Bis:

Q: Suppose h is continuous on ℝ and h(q) = 0 for every rational number q. Does it follow that h(x) = 0…

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (If…

A: Follow 2nd step.

Q: let f (x) = -, over the interval 0<x<2n , find b . 1 - .a O 1 .b O 1 .c O 1 .d O

A: given function is                                              f(x)=x2, 0&lt;x&lt;2π we have to find…

Q: about each graph. r(x) r(-1)=. r(x)= 4, x=, r(2)%=. On what interval is r(x)<7?

A: Linear equations

Q: Suppose f : (a, b) → R is continuous at every point in the open Question 3 interval (a, b), and that…

A:

Q: Let A be a cut. Show that if r ∈ A and s /∈ A, then r &lt; s. To dispel any suspense, let’s get…

A: Consider the definition for the Dedekind cut A.

Q: Let R, - {r E R|1 5 x3 x < 1 for each positive integer i. (Enter your answers using interval…

A:

Q: Let a1 > 0, a2 > 0, with a1 + a2 = a. Then X - H al n Zaz) = 1 - a P a. Use this equation to derive…

A: Solution: Part a) The following equation is given to derive a more general expression for a…

Q: Let D, = {x € R|1sIs1+} %3D = 1,1 +for each positive integer. Find the following and enter your…

A:

Q: On which of the following intervals is fx)=x*-100x2+x-10 concave up? OA (-inf,-5) O B. (-inf,-4)…

A: We will use second derivative test to check concavity

Q: Choose the correct intervals of x and y such that (x+y)³ is greater than 8. O A O B x> or y > Oc y>…

A: Y’’ +4y’+ 5y=35 e-4x      y’(0)=1  --&gt; i) Therefore, (D2+ 4D +5)y =0 is homogenous The auxiliary…

Q: Given that f(x) = x²({/28 – x2), and max on the closed interval [-1, 6] use the techniques discussed…

A: 2)  Given function:  fx=x228-x23 on the interval [-1,6].

Q: Suppose that the functionss and t are defined for all real numbers x as follows. s (x) = x t (x) =…

A:

Q: Which of the following functions satisfy the inequality q(x) <0 only on the interval - 5, 9]? O q(x)…

A: which of the following functions satisfy the inequality

Q: Given the interval (a,b), on the x-axis with the point c inside, find the greatest value for 8 >0…

A:

Q: Q3/ By using definition, proof that cot x = - csc² x. xp

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Q: For what values of a, m andb does the function 3, x 0 0 <x <1 f(x) = - тх + b, x²+3x + a, %3D 1<x< 2…

A:

Q: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

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Q: Consider the following intervals on R: A = (0, 1); B= (1,2); and C = [2, 3). Determine if every pair…

A: Solution

Q: 62. Let D be the domain bounded by y = x2 +1 and y = 2. Prove the incquality 4 20 (x² dA 3

A: The domain is y=x2+1 and y=2. Sketch the domain D as shown below.

Q: 45. Let f(x) = e¯* and T3(x) = 1- x + Use the error bound to show that for all x > 0, x4 If (x) –…

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Q: Suppose that the functions s and t are defined for all real numbers x as follow s (x) =x-3 t (x) =…

A:

Q: Given g(x)= sqrt(1-x2), is g Lipschitz on whole the interval [-1,1] ?

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Q: If f:R to {0,1} and I is an interval on which f has both values , the f has a discontinuity in I.…

A: Given that f has both 0 and 1 in its range.  This means there will be some x and y values for which…

Q: Use an appropriate theorem to complete the following statement. If f is differentiable and f(3) <…

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Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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Q: O No, because f is not continuous on the closed interval [a, b].

A: Given that: The function f ( x) = x2 - 81x - 4     ,  [ -9, 9  ]  .

Q: Determine whether Rlle's Theorem can be applied to fon the closed interval. If Rolle's Theorem can…

A:

Q: 1. Consider the following intervals on R: A = (0,1); B = (1,2); and C = [2,3). For each pair of…

A:

Q: The domain of the function fod- tanh(17-) is (A, 198), Then The value of k- The value of A=

A: Let us consider the given function f(x)=tanh-1x The domain of the function is  x∈(-1,1) The range of…

Q: Verify that the function satisfies the three hypotheses of Rolle's The orem on Hhe given interval.…

A: Since f(x) is a polynomial function and so it is continuous on closed interval [0, 2] and…

Q: Define Floor: R → Z by the formula Floor(x) = for all real numbers x. Here are some example values:…

A: See the proof and counter example below.

Q: Given the interval (a, b) on the x-axis with the point c inside, find the greatest value for 8 > 0…

A: The objective is to find the correct option.

Q: Express the set W = {q|q 2} using interval notation. Use "U" for or .

A:

Q: 3. On which of the following intervals is f(2) increaaing? Choose all that apply (a) (0, 1) (b) (0,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 3x s(x) =…

A:

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: fx=x3+8,  -9, -6,  fc=6 Since the cube root function is continuous everywhere, therefore given…

Q: (2) Show that C(0, 1] C L'(0,1]. Compare |flsup and fl. Justify your answer. Generalize this to the…

A:

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s s (x) =x+1 1 (x)…

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Q: Is it true or fase ? There is a number c in the interval (a, b) such that f(c) = 0.

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Q: Let [a, b] and [c, d] be intervals satisfying [c, d] C [a, b]. Show that if f E R(a) over [a, b]…

A: Given that a, b and c, d are intervals satisfying…

Q: Let a, x, and y be real numbers and let e > 0. Suppose that |x-al < e and y-al <e Use the Triangle…

A: Given that, a, x, and y be real numbers and let ε &gt; 0Also,x-a&lt;εand y-a&lt;εWe know…

Q: For what values of a, m and b does the function x = 0 0 <x<1 3, f(x) = }-x? + 3x + a, (mx+b, 1<xS2…

A:

Q: Let C be the Carve of intersection Z - l-2x2 and cyhder x* ys 1 oniented counter dockwise from…

A: Given  F→=4x2+4xy2,4xy+z and the curve of the intersection z=1-2x2 and cylinder x2+y2=1 oriented…

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: fx=x2+xx-1, 52, 4,  fc=6 Given function is continuous in the interval 52, 4. Now,…

Q: Suppose the function f has the property that there exists a number B such that |S(x) – f(c)| < B|x –…

A: Suppose the function f has the property that there exists a number B such that |f(x)-f(c)|≤B|x – c|…

Q: Which of the following is the set required for F2[x]? 35 - a) {1, (x + 1), (x + 1)²} b) {0, x, x2}…

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Q: Which of the following is not a notation for the dertvative of y In termo of x. dr f'(x) dy

A: to find the derivative we first write the function f(x) then write f(x+△x) and f(y+△y) therefore the…

Q: On which of the following intervals is f(x) = %3D concave up? X - 1

A:

Q: Let [a, b] and [c, d] be intervals satisfying [c, d] C [a, b]. Show that if f € R(a) over [a, b]…

A: Given that a,b and c,d be the interval such that c,d⊂a,b. Given that, f∈Rα So, the integral is,…