Given a function f:R → R with f(x) = x - 1, for x rational and f(x) = 5 - x, for x irrational Prove that lim-3 f(x) exist but lim f(x) doesn't exist

Q: Find the limit for when x -> 4 lim F(x), for f(x)= x2+2 ; x≠4 ; 27; x=4

A:

Q: See pencil for correction of problem

A: First we simplify the expression (x2-2x-8)/(x+2)=(x2-4x+2x-8)/(x+2)…

Q: Let f(x)={5x+1  x≠4               {1       x=4. What is f(4)? If f(4) does not exist, type: 99999…

A: The given function is

Q: Given x +1, f(x) = {Vx + 3, 1<x<4 0<x<1 7, x24 Tentukan: Determine. (a) lim f(x) X-1 (b) lim f(x)…

A: To find limits of the given function f(x)

Q: f(x+h)-f(x) In evaluating lim h-0 in f(x)= x² -1, which is the first step? h

A:

Q: lim[f(x)+ 4g(x)]

A:

Q: Suppose lim f(x) = L and lim g(x) = M. Prove that lim [f(x)-g(x)] =L-M. Xa X-a Begin by writing lim…

A: Given that limx→af(X)=L and limx→ag(X)=M . We need to prove that limx→a f(X)-limx→ag(X)=L-M. Now…

Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

A:

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

A:

Q: Prove that if lim, „a g(x) = 0 and lim, „«f(x) exists and is not 0, then %3D f(x) lim does not exist…

A:

Q: Determine the value for c so that lim f(x) exists. X-3 -7, for x3

A:

Q: Find two functions f and g such that lim f(x) and lim g(x) do not exist, but lim [f(x) + g(x)] * 0…

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: If a function is defined at a, but lim f(x) does not exist, how is x→a this shown on the function's…

A: If the limit of a function f(x) does not exist at a, then the function is not continuous at a and…

Q: Prove that if lim f(x) exists and lim [f(x) + g(x)] does not exist, then lim g(x) does not exist.

A: Given: limx→cfx exists and limx→cfx+gx does not exist, To show: limx→cgx does not exist.

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: Given: x + 1, -2 < x < 0 x = 0 0 < x < 2 x = 2 2, f(x) = -x, 0, 2 < x < 4 х — 4, What is the lim…

A: Consider the given function. fx=x+1,          -2&lt;x&lt;02,                x=0-x,…

Q: Evaluate the limit numerically: lim x → 3 f ( x ), where f ( x ) = { x 2 − 4 x + 2 x < 3 − x 2 + 8 x…

A:

Q: Show that if lim f(x) = lim h(x) = 3, and if f(x) ≤ g(x) ≤h(x) for 2-0 x-0 all z € (-1,1), then lim…

A: Given that limx→0fx=limx→0hx=3 and fx≤gx≤hx for all x∈−1,1. We have to prove that limx→0gx=3.…

Q: 4-IS. 2-x s (x)< 2Cos(x) for all x then find: lim f(x)

A:

Q: given f(x) = (x + 2x^3)^4 show the function is continuous at x = -1 by computing a.) f(-1) and b.)…

A:

Q: draw the graph of a function on [0, 5] with the given properties.

A: Removable discontinuity at any point (a) of domain of function (say f(x)) is define as Graphically…

Q: Choose the best answer for limit.

A: If we have a function f(x) and we want to find the limit of the function at x = a, that limx→a f(x).…

Q: Suppose that a function f(x) is defined for all real values of x except at r = c. Does it imply the…

A: Here we have to check whether the limit exists or not.

Q: 4. Do you agree with the following statement? When a function f is continuous at a number a, then it…

A:

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: 1/x, if x – 1 С. 1/x, if x – 1[ %3D X- -1

A: c) f(x) = 1/xx≤-1x2-2x&gt;-1limx→0f(x) = limx→0(x2-2) = 02-2 = 0-2 = -2

Q: 11. Determine the limits. In(x) a. lim X→1 X-1

A:

Q: Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6  f(x) = L, and prove that the limit…

A: Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6 f(x) = L, and prove that the limit…

Q: If f(x) > 0 for all æ and A = lim f(x) exists, then A > 0.

A:

Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

A:

Q: Let f(x) = 8x + 3. (a) Prove that lim f(x) = 27 using the formal definition of the limit. 3 (b) Find…

A: Givenf(x)=8x+3To prove limx→3f(x)Subdivision b is not defined properly

Q: Consider a function x-1 if x 1 (a) Find lim f (x) if it exists. If it doesn't exist, explain why.…

A:

Q: use the definition of differentiability f'(x) = lim- h-0 f(x+h)-f(x) h to For f(x) = %3D 6. (x-1)…

A: fx=x2x-1 Now,…

Q: す() ->a g(x) =0. +oo. Then lim- Suppose that lim,->a 9 (x) O True

A: Given :limx→a g(x)=+∞

Q: Draw the graph of f(x) = E, and annotate the graph to indicate the meaning of I-2 lim - 2| T→2 x – 2…

A: We have to find limit

Q: evaluate the limit.

A:

Q: Determine the value for c so that lim f(x) exists. x-3 f(x) = 5**, *+c, for x 3

A:

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

A:

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: Let x2 + 10x + 21 f(x) = x2 + 12x + 35 The expression using limits to calculate the equation of the…

A:

Q: 44. Prove that if lim f(x)= L #0 and lim g(x)= 0, then the limit lim 8(x) does not exist.

A: Given: limx→cf(x)=L≠0 and limx→cg(x)=0 To Show- limx→cf(x)g(x) doesnot exist. Theorem- if limx→au(x)…

Q: Find lim f(x). x2 - 16 if x>0 x+4 Let f(x) = x2 - 16 if x<0 X-4 O A. 4 О В. О Ос. -4 O D. Does not…

A:

Q: prove that lim x-2 f(x)=4 if f(x)= x^2, x does not =2…

A: Given,           To prove limx→2f(x) = 4 and f(x) =x2      if  x≠21        if x =2

Q: Suppose X⊆ R, a∈ X', f: X -> R, lim {x ->a} f(x) = L, and c ∈ R, is a constant. Use theorems to…

A:

Q: With lim f (x) = +o and lim h(x) = -∞ for any a that x→a' x→a is real number, which of the ff. is…

A:

Q: Find the limit of f(x) = 6 - 2 as x approaches o and as x approaches - o. lim f(x) = %3D (Type a…

A:

Q: Assuming that lim x→a f(x)/(x−a)2 exists, find lim x→a f(x)/x-a

A: