Identify the functions f and g such that lim f(x) does not exist, lim g(x) does not exist, but lim (f(x) + g(x)) does exist. X-0 x-0

Q: (x+ h)- f(x) In Exercises 26-27, find lim- 1-x (x) =- 26. X+2 27. (x) = Vx - 3

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Q: Let f(x) = x+1/x+2 and g(x)= 2x+3/x-1 compute: lim f(g(x))                  x>

A: fx=x+1x+2    gx=2x+3x-1   fgx=f2x+3x-1             =2x+3x-12x+3x-1 +2    +1…

Q: Given that lim f(x) = -1, lim g(x) = - 3, and lim h(x) = 4, find X 2 x2 lim [f(x) • h(x)] g(x) f(x)…

A: limx→2f(x)=-1, limx→2 g(x)=-3, limx→2 h(x)=4

Q: Find lim x→∞ h(x), if it exists. f(x) = 9x2 + 2x + 7   (a)     h(x) =  f(x) x lim x→∞ h(x) =

A: We are asked to find the limit of the function.

Q: lim f(x) = 9, lim g(x)=7 and lim h(x)=0. x → 2 x+ 2 x+ 2 Evaluate each limit, if it exists. 5g(x) a)…

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Q: Identify the functions f and g such that lim f(x) does not exist, lim g(x) does not exist, but lim…

A: Given, Two functions f(x) and g(x). To find, limx->0 f(x) and limx->0 g(x) doesn't exist.

Q: Find functions f and g such that = 0 and lim g(x) = 0, but lim [f(x) – g(x)] + 0. lim f(x) :

A: Let assume two functions,

Q: The graphs of f(x) and g(x) meet at x = 1. Evaluate lim g(x) x-1/(x)

A: Given: the graph of f(x) and g(x) meet at x=1

Q: 1. (а) Find two functions f and g and a value c such that lim[f(x) +g(x)] exists, but lim f(x) and…

A: Solve the following

Q: 6- (a) lim f(x) x--2 (e) f(x) lim x-3- (b) lim f(x) X-2+ (f) lim f(x) lim, f(x) X3+ (c)

A: According to our terms and conditions I have solved first 3 parts for remaining part repost

Q: If both lim f(x) and lim g(x) exists, then lim[f(x)+ g(x)] exists.

A:

Q: Prove that if f(x) > 0, lim f(x) = 0, and 6. х а lim g(x) = ∞, then lim f(x)s(x) = 0. х а ха

A: To prove:  Formula used:

Q: Find the value of the postive constant c, such that  lim x->infinty ((x-c)/(x+c))^x=1/4

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Q: Give an example of a function f such that lim f(x) exists but f(0) does not exist. Give also, an…

A:

Q: X,x1 Establish the existence of limf(x)· x-1

A: Given function is  fx=x,  x<11,   x=1x2, x>1

Q: Iff and g are two functions such that lim f(x) as x approaches a = + infinity and lim g(x) as x…

A:

Q: | |x| +1, x 0 (If) f(x) = {0, For what value of a, does lim f(x) exists. x -> a

A: The given function,       fx=x+1,x<00,x=0x-1,x>0

Q: Give examples of functions f and g such that lim f (x) = lim g(x), but f(x) # g(x) for all x,…

A: Limit of a function at a point is the value the function tends to as we approach the point. For…

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

A:

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: 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: Give an example where lim exists but neither lim f(x) nor f(x) X0 8(x) lim g(x) exists.

A: Given: limx→0fxgx exist but neither limx→0fx nor limx→0gx exists

Q: The limit of the function lim x → − 2 ( 2 − | x |/ 2 + x )

A: Here we have to find the value of limit limx→-222-x2+x

Q: Let f(x) = X-4 x - 4x (A) lim f(x) X→0 Find the indicated quantities, if they exist. (B) lim f(x)…

A: Please refer to the image below

Q: 38. Give an example where lim (f (x)· g(x)) exists but neither lim f(x) nor lim g(x) exists.

A: Let fx=-1  for x≤11     for x>1 and gx=1fx  i.e.  gx=-1  for x≤11     for x>1

Q: Find  lim x→∞ h(x),  if it exists. f(x) = 3x2 + 2x + 1   (a)     h(x) =  f(x) x lim x→∞ h(x) =

A:

Q: Let f, g and h be functions defined on R \ {0} such that both f and h are even functions, g is an…

A: f and h are even function and g is an odd function

Q: Using: lim f(x) = 5 and lim g(x) = 5, evaluate %3D x-3 x-3 lim x-3 f(x)+ g(x) 3f(x) Limit = B..

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: (a) If lim f(x) exists then lim f (x)² exists. (TRUE)

A: Given that  limx→cf(x) exists Let us consider limx→cf(x)=L To prove that,  limx→c(f(x))2 also exists

Q: x3 - 1 (x + 1)2 Let f (x) = Find lim f(x)? | x² - 5x + 4 x² + 1 X-1

A:

Q: Let lim f(x) 3 and lim g(x) = 8. Find lim ( 4· f(x) – 2 · g(x) x→a x→a x→a

A: Solve by using difference rule of limit

Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) = x-3 (b) lim g(x) =| x-2 (c) lim g(f(x)) : %3D

A: Given, f(x)=x+3 g(x)=x2

Q: Determine the value for c so that lim f(x) exists. x→5 1 f(x) 5*+c, for x 5 The value of c is. II

A: Given function: fx=15x+c,     for x<5-x+9,      for x>5

Q: Give an example of two functions f and g such that limx->0f(x) and limx->0g(x) do not exist, but…

A: Give an example of two functions f and g such that limx->0f(x) and limx->0g(x) do not exist,…

Q: Find lim,-2 f(x) 2 -3 -2 -1 2 3 lim→-2 f(x) = 0 %3D lim, -2 f(x) = 2 lim,-2 f(x) = 1 Does Not exist

A:

Q: Let lim f(x) = 3 and lim g(x) = - 5. Find lim [f(x)+ g(x)². X→a

A: Applying the limit inside the square.

Q: Determine whether the statement is true or false. f(x)] If lim f(x) = 0 and lim g(x) = 0, then lim…

A: If limx→1f(x)=0 and limx→1g(x)=0 then limx→1 f(x)g(x)=limx→1 f'(x)g'(x).  This is L'Hospital's rule.…

Q: x 0 Can also be displayed as: f(x) = [x - 1 when x < 0, 1 when x = = 0, x² 1 when x ≥ 0] For this…

A: The given function,     fx=x-1,x&lt;01,x=0x2-1,x&gt;0

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

A: NOTE: Refresh your page if you can't see any equations. . find the left side limit of the function…

Q: find the limit if it exists if it does not exist explain why. If: x² +x - 6 |x-2| g(x)%3D a) Find:…

A:

Q: Evaluate lim 7(&+h)-}(x) for the given value of x and function f. h h→0 f(x)= +7, x= 10

A: We have to find the limit

Q: Sketch the graph of a function f for which lim f(x) = 0 • lim f(x) = - ∞ I5+ lim f(x) = - 5 %3D エ→-。…

A:

Q: Identify the functions f and g such that lim f(x) and lim g(x) do not exist, but lim f(x) does…

A:

Q: a) lim,-1- F(x) = b) lim,--1+ F(x) = | %3D c) lim,--1 F(x) =| | d) F(-1) = %3D e) lim,1- F(x) = %3D…

A: We have to find

Q: Determine lim f(x), lim f(x), and lim f(x), if it exists. 3-x x5

A:

Q: 1. Determine if lim f(x) exists or does not exist. f(x) = {6 if x>0 If x < 0 2. Evaluate lim f(x),…

A: Limit at x tends to 0 is not exists because right hand limit is not equal to left hand limit.  Limit…

Q: Find the limit, if it exists. [x2 – 16 :- 16 if x>0 Let f(x) = x - 16 x- 4 if x<0 Find lim f(x) x-0+…

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Q: Identify the functions f and g such that lim f(x) does not exist, lim g(x) does not exist, but lim…

A:

Q: Given that lim f(x) = 4 and lim g(x) = -2. Find the value of x-2 x-2 lim 4f(x) + x-2 [g(x)]³ ) 2

A: we find the value of given limit