Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| <

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A:

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: Express the set of numbers x satisfying the given condition as an interval. |3x + 5| &lt; 1

A: 3x+5&lt;1

Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

A:

Q: 2) (a) Verify that the function f(x) =x3 – 3x + 2 satisfies the hypotheses of the Mean Value Theorem…

A: to verify the Mean value theorem over interval [-2, 2] for following functionf(x)=x3-3x+2

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Q: Show that f1x2 Vin x is right-continuous at x = 1.

A:

Q: Evaluate (x by Simpson's rule breaking it into 6 intervals. 1 2+x2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: 2, if x -1 Find the value for a and b such that f (x) = {ax + b, if – 1 3 for all real numbers.

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous at x=-1 so we…

Q: 4 ,5 Let f(x) = 7x* In(x) f'(x)

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Q: 9) State the intervals of increasing and decreasing behavior in the function k(x) = x2 In x?.

A:

Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

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Q: _25. Determine if f (x) = {"" (2x – 1 if x 5 is continuous on [2,5]. A. discontinuous on an…

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) = if 2 < x…

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Q: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| < |3

A: Given that |x2-1|&lt;13 That is -13&lt;(x2-1)&lt;13

Q: Determine the absolute extreme values of f(x) = 5x – 10~/x on the interval [0, 16].

A:

Q: if x = 0 11. f(x) = x - 1 if 0 < x < 1 In x if x = 1 et

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 5. Check the continuity of r+5| 2x+10 x + -5 f(x) = x = -5 at x = -5.

A:

Q: (3) Show that the function is discontinuous on the specified interval. Vx2 - 64 if x < -8 if -8 <x <…

A: Note: According our answering guidelines we have to answer only one question (if there are multiple…

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

A:

Q: 9. The interval for function (6-x)/4< (3x-4)/2 is

A: Find your answer below

Q: Prove the inequality tanx2/tanx1&gt;x2x1 provided 0&lt;x1&lt;x2&lt;π2.

A: Define a function f(x) = tan / x Differentiate both sides w.r.t x to get,

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

A:

Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

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Q: prove using the IVT. √2 exists. Hint: Consider f (x) = x2.

A: we have to show √2 exists. Now let

Q: 21. Discuss the continuity of: for for 0sx 2

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Q: express the set of numbers x satisfying the given condition as an interval.       lxl ≤ 9

A: Given: x≤ 9 Express x≤ 9 in terms of interval

Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

A:

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: (х — т 11- тх if x < 3 if x 2 3 5) Find m so that g(x) = Is continuous for all x?

A:

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

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Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Find the extreme values of f(x) = In 1+x SOUITION

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Q: Show that x+1/x is increasing on [1,∞]

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

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Q: 1 Express the domain of f(x) using interval notation. Use oo for oo and use U to combine 2 - 2 – 3x…

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Q: Find all numbers, c, that satisfies the Mean Value Theorem for f(x) = x3on [1, 4].

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Q: 1- f(x) = x³. ammmed

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

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(1) = 0

A: We have, f'x=2x Integrating both of the side with respect to x, we get the result as…

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

Q: Find absolute extrmum(if any) f(x)=x2-4x+5 on [-2,3]

A:

Q: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

A: Solved below

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: "8 does not divide x^2– 1 if x is even". prove it directly

A: We need to prove  8 does not divide x2 - 1 , if x is even. OR if x is even, the 8 does not divide x2…

Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.