A function f: [a, b] → R is of bounded variation if and only if there is some V > 0 such for all a < xo S ¤1 S... Xn S b, EIf (Tk) – f(2k+1)| S V. k=1 Show that f can be written as difference of two monotone functions.

Q: lim f(x, y) = f(a, b). (x,y)→(a,b) If f is a rational function, then Select one: True False

A: To find the given statements are true or not.

Q: 5. Prove that the function f: Z → Z defined by f(x) = 3x + 1 is one-to-one.

A:

Q: In this excercise · solve the given system by back substitution. 23.2₁ + 1₂ = 23-24 = 1 на тиз тии…

A:

Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

A:

Q: Determine the range of f, if f: D → R, where f(x) = x². I. D = (-2,2) II. D = [-7,2] III. D = (-4,2]…

A: I. D = (-2,2) Here the variable x lies between -2 and 2, that is,…

Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

A:

Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

A:

Q: Evaluate fff f(x, y, z) dV for the specified and B: B f(x, y, z): Z | 8 2 ≤ x ≤ 6,0 ≤ y ≤ 6,

A: We have to find the value of the given expression according to the given information

Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

A: Answer

Q: Show that the following relations are not functions on R. a) ƒ = {(x, y) = RxR | y=x/(x² −7x+12)}

A: Given function. y=xx2-7x+12 is not define for x2-7x+12=0 =&gt; (x-3)(x-4)=0

Q: f :R →R, f(x) = 3 + ax² + bx +11 fonksiyonu (-3,5) aralığında 20 - azalan ise atb-kaçtır ? If the…

A:

Q: Q.10. Let [a, b] be an interval of R. Let f:[a,b]→R be a function such that f is M-times…

A:

Q: Test the series for convergence or divergence by applying the Limit Comparison Test.

A: Explanation of the answer is as follows

Q: (c) Evaluate the Riemann integral ₁¹(x) dx by using definition with the parti- tion 2n=1,2}, n+1 =…

A:

Q: O Find the largest value of A such that the function f(x) = x + 1x? - 4x + 6 is decreasing for all x…

A:

Q: let F be the function from R to R defined by: f(x) =x². Find f–¹({1})

A:

Q: Determine the domain and range of the function f: {r,s,t,u} ➔ {A,B,C,D,E} defined by f(r) = A, f(s)…

A: Domain of a function is the set of possible values of independent variable. The domain of given…

Q: Let f(x) = x³ – 6, – 3 < x < - 1 The domain of f- is the interval [A, B 1 where A and B = %3D

A:

Q: (b) Determine the range of f, if f :D → R, where f (x) = x?. I. D = (-2, 2) II. D = [-7, 2] III. D =…

A:

Q: Let f : R → R be defined as                   f(x) = 10x + 7. Find the function            g : R → R…

A:

Q: If a < c < b and f(c) is the greatest value on the interval (a, b), then f(c) is a ....

A:

Q: Consider the functions f, g given by f(y) = Ay, g(x) = Bx where A is m × p and B is p × n. In…

A:

Q: Evaluate the Riemann integral f'(x) dx by using definition with the tion = {₁,"+11/ n Pn= i=1 n+1…

A: Given Data: Let the function f:R→R be defined by fx=-1x2x≠0,0x=0To evaluate the Riemann integral…

Q: The function f(x) = x² + 1 satisfies Rolle's Theorem in the interval [-2, –0.5]. - x² Select one: O…

A:

Q: 4. Show that the function f: R → R defined by f(x) = x² - 3x + 1 is not one-to-one.

A: