Given the conditions below, a function f is said to be continuous at "a" if (1) f(d) exists; (2) lim f(x) exists; and (3) lim f(x) = f(d).

Q: Give the equation(s) for a single function, f(x), that satisfies all of the following: lim f(x) =1…

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Q: Given the function f ( x ) = 1 /(x + 3) . Find  lim Δx ⟶ 0 (f ( x + Δx ) − f ( x ))/ Δx

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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: 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…

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: If f and g are continuous functions with f(-3) = 4 and the following limit, find g(-3). lim [4f (x)…

A: Given: limx→1f(x)-4x-1=7 Also f and g is continuous function with f(-3)=4  and limx→-3[4f(x)-g(x)]=9…

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: Sketch the graph of a function with the given limits.

A: Given the function with the limits.

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: 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. Is the function continuous at the point being approached? lim 2. Cscx+23…

A: We have to solve the limit and  check weather it is continuous or not

Q: Let f(x) = (1 + x)1/x. (a) Estimate the value of the limit lim (1 + x)1/x to five decimal places.…

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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: In terms of limits, what does it mean for f to grow faster than g as x→∞? Choose the correct answer…

A: We need to choose correct option.

Q: Consider the function: f (x) · g (x) = 15x · tan 12 What is lim f (x)· g (x)?

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Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

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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: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

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Q: If you know in advance that lim f (x) exists, can you determine its X+5 value from a plot of ƒ for…

A: Given that limit of f(x) exists at x=5.That means the function f(x) is continuous and differentiable…

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

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: Use the graphs of f and g and their tangent lines at (2, 0) to find lim f(x) x+2 g(x) y4 y = 1.6(x -…

A: We need to evaluate the value of limx→2f(x)g(x) using the following graph

Q: Sketch a possible graph of a function that satisfies the conditions below. (0) 0, lim f(x) - 1; lim…

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

A: Given thatf is continuous To determinelimx→1f(x)

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…

Q: Find a formula for a function f that satisfies the following conditions. lim fx) = 0, lim f(x) - -0,…

A: Function

Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

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Q: If Lim [x3 – g(x)] = 12 as x tends to 3, use the Rules of Limits to find Lim g(x) as x tends to 3.…

A: Given: limx→3x3-gx=12

Q: Is the function continuous at x = -3? If not, what type of discontinuity occurs? Explain. 6. lim…

A: Given query is find whether function is continuous or not on x =-3.

Q: When lim f(x) exists, it always equals f(a). State whether this statement is true or false. Xa

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Q: 4 Use the following graph of f(x). 2- a. find the limƒ (x) x--3 b. find the lim f (x) -2- c. is f(x)…

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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: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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Q: Make a table of function evaluations near the limit and use this to estimate the value of the limi…

A: Given: f(x)=limx→0xsin)(x)

Q: Find the limits of the functions below a) limx-3 x* sin x b) lim,

A: We can find the limit of both the question as below.

Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: If limxS1 ƒ(x) = 5, must ƒ be defined at x = 1? If it is, must ƒ(1) = 5? Can we conclude anything…

A: Given limx→1fx=5

Q: If 2 - x2 <=g(x)<= 2 cos x for all x, find lim x-->0 g(x).

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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: If + 1for all positive x-values, then what is lim f(x)? X- 4

A: We have to find limit

Q: Suppose that f (x) is a function such that lim f(r) and lim f (r) both exist. Does this mean lim…

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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: 1. For any function f(x) such that the number a is in the domain of the function, lim,→a f(x) = f…

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Q: The graph of a function f and its tangent line at 0 are shown. What is the value of lim X→0 e7x f(x)…

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Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

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

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Q: Let f(x) be the function defined by x²+ 4x (xs3) 2x - 1 (x>3) the rule f(x) Find the one-sided limit…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.