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## Related Calculus Q&A

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Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

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

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Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

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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: 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: Using the graph of f(x) given below lim f(x) = x→2 O 2 O 1.5 1 does not exists

A: Graph of the function is given, we have to find the value of limit at x=2

Q: Determine the value for c so that lim f(x) exists. X-4 x2 - 9, for x4 The value of c is

A: Click to see the answer

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Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

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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,…

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Q: b) The function g is defined by 4 x-2 x+ 2 Show that lim g(x)exist. -2

A: Please refer to the image below.

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Q: 2. a. Draw a graph with the following characteristics: lim f(x) = 3 X->2* lim f(x) = 0 %3D x-→2 f(2)…

A: The graph has the properties,limx→2+f(x)=3limx→2-f(x)=0f(2)=3limx→-1f(x)=-2f(-1)=1

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Q: 1 Let F (x) = 1 +2 2< Find lim F (x). 2+

A: Click to see the answer

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Q: The lim(x0) [f(x)] fails to exist because.. (refer to the graph below) * As the function approaches…

A: Click to see the answer

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Q: . Sketch the graph of the f(x) function and use it to determine the values of a for which lim f (x)…

A: Click to see the answer

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Q: Given that lim f(x) = 4 X-3 lim g(x) = -5 X-3 lim h(x) = 0, X-3

A: Click to see the answer

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Q: If the limit of two different functions, lim f(x) and lim g(x) XC exist, then so does lim[f(x) -…

A: for example limx->2f(x)= 5limx->2g(x)=∞ f(x) and g(x) exists now find the limit f(x)-g(x) when…

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Q: (1) Evaluate the limit, if it exists. (a) x² + x - 2 lim t→1 x² - 4.x + 3 (b) x - 81 lim x→81 Vx - 9

A: Click to see the answer

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Q: Use the graph to evaluate the limit. 3) lim f(x) x-0 3) 3+ 2+ -4 3. 4 X 4) lim f(x) x-0 3+ 2- 10 -3…

A: Click to see the answer

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Q: [3 3. Consider f (x) =- 2х - 3 if x< 0 Find lim f(x) if x20.

A: To determine the limit of the function.

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Q: e2h-1 if f'(a) lim-0 what is f(r) and what is a? h

A: Click to see the answer

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Q: 22. If lim f(x) = 18 and lim g(x) = -1.5, find the lim %3D %3D x-a L4g(x). xa А. 6 -3 С. -1 D. -7 В.

A: 22) If limx→afx=18 and limx→agx=-1.5 , find the limx→afx4gx

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Q: 19) Find lim f(x) %3D 19) X2 + A) 2 B) – 2 C) - 4 D) - 8 20) Find lim f(x) 20) X 2

A: Click to see the answer

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Q: a. Using the Sandwich Theorem to find: lim f (x) If v5 – 2x2 <f(x)< V5-

A: Click to see the answer

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Q: Let f(x) = x³ + x² – 6x – and lim (g of)(x). 1 and g(x) = 3. Find lim(f° g)(x) x→4

A: Explanation: Given that, f(x)=x3+x2-6x-1g(x)=3 Concept Used: Composition of function:…

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

A: Click to see the answer

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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: Click to see the answer

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Q: 2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three…

A: Topic = Functions

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Consider two functions fx & gx By algebra of limits, we have, 1. limx→a fx+limx→a gx=limx→a…

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Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

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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+…

A: Click to see the answer

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Q: The lim(x0) [f(x)] fails to exist because.. (refer to the graph below) * As the function approaches…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

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Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

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Q: If the limit of two different functions, lim f(x) and lim g(x) exist, then so does lim[f (x)- g(x)].…

A: limx→cfx & limx→cgx both exist.

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Q: Let f(x) = 3x – 4 and g(x) = 8x² + 2x – 2. What is f(x) limx→-1 g(x) O a. -- Оа. O b. 7 4 1 Ос. 8

A: Click to see the answer

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Q: -3x- Consider the function g(x) = %3D 2x - 3, x24 (a) Find lim g(x) (b) Find lim g(x). (c) Does the…

A: Click to see the answer

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Q: - 5 f(x) - If lim X-4 X - 2 1, find lim f(x). %3D

A: Given limx→4fx-5x-2=1 To find limx→4fx

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Q: Find the limit. lim x→3 1−x2/(x-3)2

A: Given, The limit limx→3 1-x2x-32 We have to find the limit.

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Q: Sketch the graph of the f(x) function and use it to determine the values of a for which lim f(x)…

A: Definition of limit at a point of any function : Suppose we have a function defined on real number .…

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Q: Use the graph to evaluate the limit. 3) lim f(x) x→-1 +4+ -5 4 -3 -2 -1 +++ 1 2 3 4 5 x

A: Click to see the answer

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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

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Q: Using the graph of f(x) given below lim f(x) x→2 O 2 O 1.5 O 1 does not exists I|

A: Given graph of f(x) we find x→2lim f(x)

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Q: Suppose that a function ƒ(x) is defined for all real values of x except x = c. Can anything be said…

A: Given: The function fx is defined for all real values of x except x=c, To determine: Whether the…

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Q: State whether lim f (x) and f(c) are equal or unequal at the given value of c. Also, state whether…

A: Limiting value of the function is value that function seem to approach as it reaches certain value.…

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Q: Sketch the graph of the function. 4 + x if x < -2 f(x) = {x2 6 - x if x 2 2 if -2 sx< 2 y 5- 2 2 2 y…

A: Here, the sketch of the given function is: That is:

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Q: Find the limit or show it does not exist. 1- x2 х3 — х +1 16. lim -

A: Click to see the answer

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Q: 3. What is lim f(x)? lim f(x)? Why? X-0 AY 10 8 6. 5 -4 -3 -2 2 5 3. -1

A: Click to see the answer

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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

A: Click to see the answer

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Q: Find the limit (if it exists). |x+7-3 lim x → 2 x- 2 а. 6 b. 1

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