Prove the inequality tanx2tanx1>x2x1 provided 0<x1<x2<π2.

Q: Use logs and implicit differentiaton to prove (root(x))' = 0.5x^(-0.5)

A: Let y = √x Take log to the base e, i.e. natural log, i.e ln on both the sides, ln(y) = ln(√x) =…

Q: B) Let f:R - R be defined by. 3 if x rational number. f(x) = if x irrational number !3! Show that f…

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Q: 2- Can the False Position Method be used to find the root of f(x)=, starting with the interval…

A: Given that  f(x)=1/(x-3) To find the roots of the equation by using false position method

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: /2+ x² 2) Lim X

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Q: 4. [5] Please find in interval notation the values of x for which this expression is real. Show…

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Q: Show that there is a solution to the following equation in the interval (2,3). (Hint: Use the…

A: Since there are two questions posted, we will answer the first question (1). If you want the second…

Q: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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Q: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: What are the zeros of f(x)=2cos(3x)+1 on the interval [0,π]?

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Q: Express the set of numbers x satisfying the given condition as an interval. |4x − 1| ≤ 8

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Q: Use intermediate value theorem to show that f(x) = -x3 + x2 + x + 1 must have at least one zero on…

A: Given: fx=-x3+x2+x+1 &amp; interval 0,2 To show: The given function must have at least one zero on…

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(-2) = 3.

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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: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

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Q: Show that there are an infinite number of rational numbers between any two real numbers x and y with…

A: using Archimedean property to prove above therom...

Q: find the interval of existence in which the particular solutions of the IVP is vaild

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Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: th term in the exp ansion of x 20, then r is?

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Q: Prove that f(x) =- 2x(sinx+ tanx), is an odd function, where [] denotes %3D X+ 2n -3 the greatest…

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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: Express the following in interval notation. 3. 4 < x < 19

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Q: x : x is a natural number less than 10​}

A: Write in explicit form

Q: HW4| Prove How 4 Prove if x;→ × then 6x.→6x Xj ->

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

Q: Find the domain: f(x) = In(3 – x).

A: A function is a relation which maps each element in its domain to exactly one element in its range.…

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: SolvetheInequalities and e xplain that nd showthc on the realliho tan 34X 12+3 tan 34 x 4

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Q: Prove by reductio ad absurdum that there does not exist a minimum rational number greater than zero.

A: The proof by method of reductio and absurdum mean proof by contradiction . That is , you have a…

Q: Show that f (x) = 3x² - x - 1 is O(x²) with suitable C and k.

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Q: Prove that for x&gt;0 the inequality lnx≤x−1 is true.

A: Given data:     The given inequality is: . The given expression can be written as, Here, f(x) is…

Q: 4) Find the intervals where the function g is positive and enter exact answers only in interval…

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Q: Find the term of (x + +)° that does not contain x.

A: Given expression is, x+1x6. The general term is given by, Cknakbn-k. In the given expression,…

Q: Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving…

A: The given data is: Prove that fx=4x-22x has at least one real zero in the interval 1,2 without…

Q: on is discontinuous on the specified interval. Vx2 - 64 if IS -8 if-8<x<8 88] 0 ifx28 f(x) = {x+8

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Q: Use the Intermediate Value Theorem to show that 2х - 3 if – 3 0 has a zero on the interval [-2, In…

A: By using the Intermediate Value Theorem to show that fx=2x-3x+3  if -3&lt;x≤0-3+2 cosh x  if…

Q: 6. Prove from first principles (with ac- 6 argument ) that लेग ½ lim 7--1

A: 1x2+1-12=2-x2+12x2+1                               =2-x2+12x2+12+x2+1…

Q: Use the Intermediate Value Theorem to show that f (x) = x5 + x3 − 5x + 2 has a root (that is, takes…

A: Given equation is

Q: 8) Find what va lues of x salisfy the fellowing inequality: 3x -1 >2 2x +5

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Q: 7. Use the Intermediate Value Theorem (IVT) to show that there is a root of the equation In r = 3 –…

A: We can use intermidiate theorem in order to solve the given problem.

Q: Use the IVT to find an interval of length 0.3 that contains a root of In r = 3 – 2r.

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

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Q: Show that cosh x> 1 + x² for all x.

A: comparison

Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

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

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Q: 29. For |x|<1, prove that 16x 24x 8x 1 + 1-x1+x 1-x ..... .. 8x 8x = 1+ (1- x)? (1+x)²' (1-x)?

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