Prove that for x≠0 the inequality ex>1+x holds.

Q: Solve the following inequality graphically in two-dimensional plane:y < – 2

A: We first draw y=-2 line

Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

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Q: Solve the following inequality graphically in two-dimensional plane: x > – 3

A: We first draw the line x=-3

Q: Prove that the Intermediate Value Theorem remains true when the inequality sign is flipped, i.e.…

A: We know that According to Intermediate Value Theorem: A function is continuous in interval  I = [a ,…

Q: Determine the interval(s) on which x2 + 2x – 3 > 0. - Ох1 Ox 1 -3 1

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Q: a. Prove that ex>= 1 + x if x>= 0. b. Use the result in part (a) to show that ex>= 1 + x +…

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Q: Use interval notation to represent all values of x satisfying the given condition. y = 1 - (x + 3) +…

A: y=1-x+3+2xy is atleast 4 i.ey≥41-x+3+2x≥41-x-3+2x≥4

Q: Show that for all x>0, e* >1+x+÷ 2.

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Q: Prove that if both y and z are solutions to x' = Ax, then for any c1, c2, the function c1y + c2z is…

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Q: : 2 < x < 4} and B = {x € R : –4 < x < 1}. Prove

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Q: If f'(x) and g'(x) exist and f'(x) > g(x) for all real a, then the graph of y = f(x) and the graph…

A: In this question we have to find how many time functions will intersect to each other.

Q: Find (with proof) the infimums of the sets S = {1 / n : n  ∈ ℕ} and T = { (-1)n / n : n  ∈ ℕ}. Is…

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Q: Show that the interval [a,b] is complete

A: Given

Q: 2. Consider a ball thrown in the air (f) defined by the formula f(x) = (3 + x)^2 whose domain is the…

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Q: Suppose that the possible values of æ is the interval (-3, ). This means that: - x -3 -3 < x < 3

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

Q: f x and y are two positive real numbers, then there exists a positive integer n such that ny>x

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Q: Prove the inequality tanx2tanx1&gt;x2x1 provided 0&lt;x1&lt;x2&lt;π2.

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Q: Which inequality describes the restrictions on x according to the hinge theorem? 5x 95 5x + 3 3x+17…

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Q: 4. Find all values of x satisfying In[(2x + 1)(x +2)] = 2 In(x+2). Verify the values of x you found…

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

A: Write in explicit form

Q: o Yes, zero is contained in the interval.

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Q: Suppose that X~ N(100, 20). For some valle x, we have that P(X ≤ x) = 0.7605. What must be the value…

A: given data x~N (100,20)here μ = 100σ=20p(X≤x)= 0.7605we have to find out the value of x for given…

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

A: To solve the inequality: 3x+5&lt;1 Solution: We know that if x&lt;a then -a&lt;x&lt;a. We have…

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

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Q: Prove the following inequality. Do not evaluate the integral. 1 ,1 - x² + x +1 | - 2 0, 1+ x4 4

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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: Let ƒ(x) = x² + 2 x – 2. Find all the values satisfying f(x) < x² + 2. - NOTE: Enter an inequality…

A: Given f(x)=x2+2x-2

Q: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: Verify that f(x)=x2+1/x satisfies the hypotheses of the Rolle's Theorem on the interval [1/2 2] and…

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Q: Prove thot if yef(x) is continyous and f(x) =0 when x is a ratsonal number, then f(x) =0 for all x €…

A: Given that y = f(x) is continuous and f(x) = 0, x is a rational number. To prove f(x) = 0 for all…

Q: Show that o () –1 is an implicit solution to 2 -2y on the interval (-00, 00). Inload our

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Q: The solution set for x satisfying both 1| 1 - is O a) None of these b) (-∞, – 1) U (1, 3] ОФ (1, 3]…

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Q: a) Verify Rolle's Theorem for ƒ(x)= 2.x' – 8.x + 4 over the interval [0,2].

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Q: Show that the interval [0, 1] is uncountable.

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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: Solve the following inequality graphically in two-dimensional plane:3x + 4y ≤ 12

A: We first graph 3x+4y=12 line We make a table for it x 4 0 y 0 3

Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

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Q: Let xE [0,1] and n E N, show that the following inequality holds x2 x3 3 1+x + 2! 3! +.....+ n! (n +…

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Q: Label

A: True

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

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Q: Use the mean value theorem to establish the following inequalities: x-1 b) 1 -

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Q: 3 Prove that Var(aX– b) = a² Var(X) where a and b are constants. %3D |

A: We know that the V(X) =E(X2) -(E(X))2 By using the  above definition of V(X), we can easily prove…

Q: The Intermediate Value Theorem can be used to prove that the equation 2²-2-15-0 has at least one…

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Q: Show that f (r) = x³ – 3x2 + 2 is monotonically increasing on every interval.

A: Given that: f(x)=x3-3x2+2

Q: B.Discuss the continuity of 1 x +- for x <0 y = -x3 for 0 < x < 1 -1 for 1 < x

A: The objective is to discuss the continuity of the given function.

Q: (b)Prove the inequality x² + x² + ... + x² n AI 2 xn ( ³²₁ +2²₂ + ... + x n ) ² n

A: Sol

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

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