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 does exist.

Q: (a) lim f(x) x-1 (Ь) lim f(x) x 3- lim f(x) X-3+ (c)

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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: 4-x V6-5x+x f(x) = 1- find the domain 2- find lim f(x), lim f(x), lim f(x) x2 x-2 x-+2

A: givenf(x)=4-x2x2-5x+6solving x2-5x+6 by factorization method=x2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)and…

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

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Q: If g(x) is differentiable at x = 1, then lim g(x) = g(1). x+ 1+ True False

A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

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

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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: Find lim h(x), if it exists. X> 00 f(x) = 3x + 2x + 3 (a) f(x) h(x) = lim h(x) X> 00 f(x) (b) h(x)…

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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.

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Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

Q: Find the limit, if it exists. (x² – 16 if x>0 Let f(x) =x2 -16 if x<0 x- 4 Find lim f(x). x-0- 00 -4…

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Q: lim 극 et – 1 x-1

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Q: A = lim R, = lim [f(x1)Ax + f(x2)Ax+.+ n-00 x< 10. Using the above definition, determine whic

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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)]…

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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: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

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

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Q: -f(x): a. lim

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

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: f(x) is said to be 2c g(1) If lim f(x) = 0 and limg(x) = 0, then lim- or more specifically, a 0/0

A: we have been given  limx→cf(x)=0 and limx→cg(x)=0 then    by using the quotient rule property of…

Q: Show by example that lim[f(x) +g(x)] can exist even if lim f(x) and lim g(x) do not exist.

A: Let,  f(x)=1x-c, g(x)=1c-x

Q: Evaluate the limit given

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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: If f(x) < x² for all æ E R and lim f(x) exists, then what can be concluded about lim f(x)? a. lim…

A: we have to find the following

Q: Given a function f:R → R with f(x) = x - 1, for x rational and f(x) = 5 - x, for x irrational Prove…

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Q: Give examples of functions f(x) and g(x) with limx→∞ f(x) = ∞ and limx→∞ g(x) = 0

A: We want to find two functions f(x) and g(x).

Q: Find the limits. f(x) = x + 4 g(x) = x² %3D (a) lim, f(x) %3D (b) lim g(x) * X--4 %3D (c) lim…

A: Given,            fx=x+4 , gx=x2

Q: Find. 1) a. lim f(x) and b. lim f(x). x-0- Find the limit, if it exists. x2 + 4 2) lim X-2 x+2 3)…

A: Here function is given and we need to find limit

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

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

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

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Q: a) lim- 1 3x +x+1 -x +5x b) lim f(x) where f(x)={ (4x xs2 3x x>2 sin 2x c) lim g(x) where 2+x < g(x)…

A: alimx→∞−x2+5x3x2+x+1Divide and multiply by x2limx→∞x2−x2+5xx2x23x2+x+1x2limx→∞−1+5x3+1x+1x2=−13

Q: Evaluate the limit given

A: Given:

Q: Find lim h(x), if it exists. X- 00 f(x) = 3x2 + 2x + 9 f(x) (a) h(x) lim h(x) = X- 00 f(x) h(x) = x2…

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Q: a. lim f(x) b. lim f(x) x→4+ c. lim f (x) 1. x-4 X→4-

A: Given query is to find indicated limits.

Q: Use the limit properties to find the following limit.

A: Given that, limx→3fx=3      ...(1)limx→3gx=2      ...(2)

Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

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Q: Let f(x)=x'e* the value of lim [f (x) is: 4 x 1 a) 1 b) | e

A: Given   f(x)=x2ex2 We have to find 14limx→-1f(x)1x

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

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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: 1-x if x 0 x+2

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Q: x -1 ifx1 (a) Find lim f(x) if it exists. If it doesn't exist, explain why. (b) Find lim f(x) if it…

A: Given query is to find indicated limits.

Q: H Let f(x) = 0 if x=2 x² −1 if x > 2 Determine the two-sided limit lim fƒ(x). x-2

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Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.

Q: Sketch the graph of a function f such that: limf(x)=0 X-7

A: We take a function  f(x)= 1/(x-7)

Q: Evaluate the limit given

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

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