Graph the function (1 x<-1 -x -1

Q: 1 lim x x→0

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Q: Find the limit and discuss the continuity of the function.

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Q: 2. Construct a table of values to investigate 1 if x -1

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Q: What can be said about f (3) if f is continuous and lim f(x) = ?

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Q: х+3if x1 6. lim x→1 f(x) f(x)

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Q: 4л — 6, 2 <г -

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Q: The FunctionF(x)=4x^3-5x+1 is both continuous and differentiable at x=2. Write this facts as limit…

A: Given :F(x)=4x3-5x+1

Q: Determine the limit by sketching an appropriate graph. - 5x - 4 for x<2 lim f(x), where f(x) = . 4x…

A: The limit in the question have asked for x-&gt;2+ which means greater than 2.

Q: Use continuity to evaluate the limit. 32 + Vx lim x→4 32 + X

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Q: Consider the following function. x2 - x - 56 f(x) = x2 + 7x Find each value. (If an answer does not…

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Q: Create a table of values for the function and use the result to explain why the limit does not…

A: Given: Function  Consider few values less than 0 and few values greater than 0 Then evaluate…

Q: Graph the function 1, x <-1 -1 < x < 0 -x, x = 0 f(x) = 1, 0 < x < 1 x 2 1. -x, 1, Then discuss, in…

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Q: lim f(x) given that |f(x)/x² + 1|< 1 x→+∞

A: Recall: Squeeze Theorem for limits:              Assume that functions f,g and h satisfy…

Q: Discuss the continuity of the function on the closed interval.

A: to find: limx→-1x3+3

Q: Consider the following function: f (x) = (x- 4)(x+2) (x +4)(x + 2) i. For what values of x is f(x)…

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Q: Determine the limit graphically, if it exists. lim f(x)= x +1+ f(x) it + 1 -5 -4/-3 -2 -1 -1- 4 5 x…

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Q: Use the definition of continuity and the properties of lim- its to show that the function is…

A: The function will be continuous if limx→a=-1+fx=limx→a=-1-fx. Consider right- hand limit…

Q: Explain, using limit definition, why f′(x) = 0 for any constant function f(x) = c.

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Q: Use continuity to evaluate the limit.

A: Given: limx→45+x5+x for evaluating given limit, we substitute x=4 in given limit

Q: Use the graph to find each limit of the graph. y 8 --- f(x) 7 3 6. 个 a. lim f(x) エ→3 b. lim f(x) =…

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Q: Use the graph to evaluate the limit. 3) lim f(x) x-0 3+ 2+ + 1 -4 -3 3 -2- -3+

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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: - 3x +4 lim -2 x - 3x + 7x - 24x + 28 a. where a is some fixed real number x = a' b. lim 2x

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Q: 2x 9. x-1 lim x-3 6-2x

A: Given limx→32xx-1-9x6-2x

Q: Prove the limit as x approaches -2 of f(x)= 10x + 19 is -1 using the definition of a limit of a…

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Q: Find the indicated limits of the following function: 11x3 – 4x2 – 8x - - f(x) = 10 – 10x – 8x3 - lim…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Create a table of values for the function and use the result to explain why the limit does not…

A: Given :  The function limx → 0 3xx2. To create a table of values for the function and to explain…

Q: Let 4 + x, if x 3 Evaluate the following expressions. lim f(x) = x-3- lim f(x) = x→3* f(3) = Is the…

A: To find the limits

Q: 2. f (x) 3 - 2x² if xくQ こ 2 メ if x 2 2

A: f(x)= x3-2x2 ; x&lt;22-x ; x≥2       a=2 , if f is differentiable , then f'(2) should be finiteusing…

Q: Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real…

A: To evaluate limit limx→110x-9-1x-1 This is 00 form. We will use L-hospital rule. In L-hospital rule…

Q: Determine if lim f(x) exists. Is the function continuous at x = 2? Show all the steps. f (x) = { 4 S…

A: Given that a function and we check that at x= 2 this function is continous or not . We know that if…

Q: Complete the table and investigate the limit. lim (x2 - 3) X -1 x approaches -1 from the left x…

A: Solve the limit

Q: Consider the following function. (4x2 if x < -1 if -1 < x < 1 4x f(x) = 4 if x 2 1 Find the…

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Q: Find the limit and discuss the continuity of the function.

A: Given  We need to : i) find the limit. ii) Discuss the continuity of the function.

Q: 1 if x-1 4. lim x→- 1 5. x f(x) f(x)

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Q: Let f(x)=1/3x+2. Use limit definition to find f'(x) algebraically

A: Solution of given question is written in below steps.

Q: Use the graph as shown to determine the following limits, and discuss the continuity of the function…

A: The function is defined by the graph given above.

Q: Use the graph to determine the limit and discuss the continuity of the function.

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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: Suppose f(x) = x2 if x ̸= 2 and is undefined at x = 2. The domain is (−∞,2)∪(2,∞). Find lim f (x).…

A: The limit exists at x tends to 2 for f(x). First of all, consider the condition for the limit to…

Q: Q5:- Evaluate the following limits x²+8-3 1. lim X→-1 x+1 x+3 2. lim x→-3 x2+4x+3

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Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why.! lim f(x), where…

A: Given the query is to find the limit of the expression.

Q: Use continuity to evaluate the limit. 12 + Vx lim x-4 V12 + x

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Q: Use limit definition to find f'(2) for the function, f(x) = 3x? – 4x + 1-

A: fx=3x2-4x+1 substitute x+h for x fx+h=3x+h2-4x+h+1 fx+h=3x2+2xh+h2-4x-4h+1 fx+h=3x2+6xh+3h2-4x-4h+1…

Q: Decide whether the limit produces an indeterminate form, lim 2x t x

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Q: 6x lim С. x→-1- \x+1 х+3

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Q: Sketch the graph that satisfies the given conditions: fis odd, f' (x) 0 for x > 2; f"(x) > 0 for 0…

A: We have to draw a graph for given conditions.