Show that || x || - || y || <= || x - y ||

Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I &lt; 2

A: Given: x+7&lt;2 We know that solution of inequalityx+a&lt;b is given by -b&lt;x+a&lt;b

Q: Find all integer x satisfying the condition x = gcd(4x + 3, 2x). Justify your answer.

A: To find all integer x satisfying the condition  x=gcd4x+3,2x

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: What are the values of a and b that make f(x)=ae^ax+bx^2+2b  x0 continuous and differentiable

A: Consider the condition for any function f(x) to be continuous at x = a. Use this condition at x = 0…

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

A:

Q: Fermat's theorem states that if f has a relative extremum and if f'(x) exists, then f'(c) = 0.…

A:

Q: Prove that = Aatilag (Elog Xi) An. %3D

A:

Q: What are the values of a and b that make f(x)=ax+a+b+1  x>0 continuous and differentiable

A:

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

A: 3x+5&lt;1

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

A:

Q: Determine whether each of these statements is true or false. Explain why. 0 ∈ ∅ ∅ ∈ {0} {0} ⊂ ∅ ∅ ⊂…

A: 1.   0 ∈ ∅ As ∅ is empty set so it can't contain any element. Hence 0 can belongs to ∅. Answer:…

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

A:

Q: 1 Let h(x) x2

A:

Q: Choose the correct intervals of x and y such that (x+y)3 is greater than 8

A:

Q: R is the amount of rain, in inches, on any particular day in 2012, and it is said to be uniform…

A: Wr want to find the probability by chebycheves inequality.

Q: Express the set of numbers x satisfying the given condition as an interval.        I x -4 I &lt; 2

A:

Q: theorem if Yet, I think I

A: 1. Ax=h+p 2.∀x.Ax 1.Universal Generalization on 3. Ax→∀x Ax  1,2 Introduction.

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: Write the formula of partial derivation with respect to x?

A: Partial derivatives  Let  f(x,y) is a function given , in which f(x,y) partially depends on x and y,…

Q: Can you help me with this?

A:

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

A:

Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

A:

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

A: to find the values

Q: et F be the collection of

A: To define, T(G)=∫G(z-y)dG(y),G∈F

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

A:

Q: f(x) x* + 3x - 3x + 2 %3D as x -00 f (x) → 0 as x -of (x) → -∞ as x +∞f(x) → -∞ as x → +of(x) → +o

A: Given polynomial f(x) =-x4+3x2-3x+2

Q: 6. Show that the half open interval [0, 2) is uncountable. (Hint: We know that (0, 2) is uncount-…

A: Since the interval (0, 2) contains the infinite subset {1.2,1.3,1.4,...} So (0, 2) is either…

Q: f(x) = In (1+x³)

A:

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: (b) Using the mean value theorem, prove the inequality, (1+x)“ >1+ ax, where a >1 and x > 0.

A:

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: On your own, verify that f(x)=e-x satisfies the conditions of the mean-value theorem on the interval…

A: f(x)=e-x on the interval [0,2]

Q: Find three positive integers x, y, and z that satisfy the given conditions. The product is 125, and…

A:

Q: Show that : [x+y] > [x] + [Y] for any real numbers x and y

A: Introduction: The greatest integer function is a significant number theoretic function. Every real…

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

A: Consider the function. Find its derivative.

Q: f(x)=In(1-x)

A:

Q: Using R, use antithetic variables to estimate the following: In(1+ x2) dt x2

A:

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

A: We have to find the domain of the given function.

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Q: Determine the intersection XN Y. Express the answ er in interval notation. X= {x |x2-2} and Y= {x|x<…

A:

Q: 2- Find ( for: y= esin-1 x

A: first derivative of function

Q: (a). Find the values of a and b that make f continuous everywhere. x² -4 if x<2 x-2 f(x)={ax² - bx+3…

A: f(x)=x2-4x-2if x&lt;2ax2-bx+3if 2≤x&lt;32x- a+bif x≥3 Definition: Continuous functionLet f(x) be a…

Q: If f(x)=sin-'x. Show that (1-x2) fx(x)-xf (x)=0. HENCE ,prove that f^(n+2)(0)=n²f^n(0)

A:

Q: Discuss the continuity of : 1 for x 2

A: Continuity

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: 1 1 2 x y x+y || +

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.