3. If f is a continuous function, what can you say about lim f(x)?

Q: If the fucntion f is undefined at x then lim f(x) does not exist. = c, C, FALSE O TRUE

A: Given- If the function fis undefined at x=c then limx→cfx does not exist. To Check- If the above…

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is…

A:

Q: evaluate the limit lim x→1+        (ln(x)) / ( ln(x − 1))

A: Given:

Q: Evaluate the limit tan x lim x →0 2x

A:

Q: For a function f, suppose lim f(x) does not exist because the left – hand and right – hand limit…

A: Given limx→c f(x) does not exist because the left-hand and right - hand limit have different values.

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: Suppose f(– 1) = 0 g( - 1) = 0 f'(– 1) = 5 g'(– 1) = 4 and all functions are continuous. lim…

A:

Q: 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?

A: the limit of a function lim f(c) = L is the same as evaluating a function f(c)

Q: 8) Suppose if x 20 f(r) = if x < 0. Identify a function g with domain R such that lim(f +g)(x)…

A:

Q: Consider the piecewise defined function x² + 2x – 1 if x 0 ° Which of the following statements is…

A: As we know that,  the function fx is continuous at a point  x=a if the left-hand limit is equal to…

Q: If a function f has no limit as x approaches c, then we say that lim f(x)

A:

Q: Can f(x) approach a limit as x ➔ c if f(c) is undefined? If so, give an example.

A: Yes .This statement f(x) approach a limit as x ➔ c if f(c) is undefined is correct. We will see one…

Q: 2 Use the definition of continuity to show f (x) = is x+3 continuous at x=1. Whenever you find a…

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Q: Can we evaluate the limit using f(c) if the constant c will not make the function undefined or…

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Q: You are given that a function f is differentiable on (-o, 0), and that lim f'(x) = 6. lim (f(x + 3)…

A: Use the mean value theorem and calculate limit in following way:-

Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

Q: Suppose that f: R→R is a continuous function, satisfying f(5)=8. What is the value of the limit lim…

A:

Q: If f is continuous from the right of x1 and lim f (x) exists, then lim f'(x) = f'_ (x1). O True…

A: it is true

Q: If f(x) is differentiable at X =c then lim f(x) must exist and f(c) must be defined

A:

Q: Consider the following function. 1 f(x): X + 9 Find the limit. lim Ax→ 0 f(x + Ax) - f(x) Ax

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Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: Find the following limit.   lim x→0+     x-12/ ln x

A:

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A: To obtain the value of limx→03x-fx4x-fx, substitute 0 for x and 1 for f(0) in the expression, and…

Q: If f(x) = tanx – x and g(x) = x3, evaluate the limit of f(x)/g(x) as x approaches zero.

A:

Q: 8. The function f(x) = 4 – x² is both continuous and differ- entiable at x = 1. Write these facts as…

A: Given that the function f(x)=4-x2 is both continuous and differentiable at x=1. To write these facts…

Q: Suppose we want to determine whether h(x) is continuous at x = 3. So far, we are given the two…

A: We have, limx→3-hx = 6 h3 = 6 To evaluate: The additional information needed which will allow us to…

Q: 1) Describe in your own words, how to determine the limit of f(x) as x approaches a given point and…

A: Hi! you have posted multiple questions. As per norms, we are answering the first question as nothing…

Q: 2. Find the limit of the following function lim (secx- tan x)

A:

Q: Suppose if x >0 f(x) = -1 if x < 0. Identify a function g with domain R such that lim (f + g)(x)…

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Q: Find lim f(x) and determine if continuous at x =2 エ→2

A: We have to check

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

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Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: If a function f is not defined at x = c, then limf(x) does not exist. True False

A: Limit of a function at a point exist mean left hand side limit and right hand side limit at that…

Q: Compute the value of the limit below by relating the limit to the definition of a derivative of a…

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Q: According to the alternate form of the definition of the derivative, to compute f′(0), we need to…

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Q: Evaluate the limit. 5 sin(x) – 5x lim x3

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Q: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

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Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=f'(0)…

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Q: 58. If f(xo, Yo) 3, what can you say about lim f(x, y) (x, y)→(xo, Yo) if f is continuous at (xo,…

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Q: Given a function f(x) = c, where c is some constant. Show that f'(x) = 0. (Hint: by limit…

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Q: If there is no single value that is approached by f(x) as x approaches a, then lim f(x) does not X→a…

A: If there is no single Value that is approached by f(x) as x approaches a,then limit of f(x) as x…

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: draw the graph of a function on [0, 5] with the given properties. 1, but lim f(x) and lim f(x) exist…

A: Let us assume that: So, f(x) is not continuous at x=1

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

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Q: Use the limit definition of the derivative f (x) – f(a) f'(a) = lim - a to find f'(a) in each case.…

A: Given fx=x3-7

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: is continuous lim x f(x) = 0 = f is continuous in 0.

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Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

A: