Is the function continuous at x = -3? If not, what type of discontinuity occurs? Explain. 6. lim f(x) = ズ→0+ 7. lim f(x) = %3D -0-ズ

Q: Q2) find the value of each limit sint 1) lim(- 1+cost +tcost C+cost x+xcosx 2) lim 0 sinxcosx

A: The limits of given functions are given as follows :

Q: A tank contains 1640 L of pure water. Solution that contains 0.03 kg of sugar per liter enters the…

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Q: 2. Given the function f(x) = ., determine if the function is continuOus or not. Identify the point/s…

A: Given function f(x)= (x2-1)/(x-1) is continuous or not , determine type of discontinue.

Q: Consider a function () whose dertvative ') continuous as shawn below Graph of f'(x), NOT f(x) 1 5 -1…

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Q: Answer the following questions. Show and explain your work. 1 (a) What type of discontinuity does…

A: a. limx→ 0+1ex-1=limx→ 0+1limx→ 0+ex-1                            =1e10-1…

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: ( 2x -. Is g(x) continuous at 2?

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Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

Q: Express the limit as a definite integral. [Hint: Consider f(x) = x*.] lim n- 00 dx

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Q: 1) For the function f whose graeh is given the value of each lihmit. If a limit dosent exise enter…

A: From the given graph :

Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

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

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

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Q: -y 2- -6 -2 -2- Given the graph of f (z) above, find the following limits. To enter 00, type ifinity…

A: Given  The graph f(x) has vertical asymptote at x=4  and horizontal asymptote at  y=0 .

Q: Find the instantaneous rate of change of each function at the given x-value. Use the form lim…

A: a) Given that…

Q: Find the instananeous rate of change for f(x)= √ X at x=1 using the limit definition

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Q: f'(x) = lim f (x+h)-f(x) h-70 f(x) %3D

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Q: (2 pts) 7. What value ofk will make lim f(x) exist? What is the limit? VI+5. ifx 3

A: given: f(x)=x+53,      if x<3kx2-4x,    if x>3 limx→3f(x) exists.

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: For what value of the constant c is the function f continuous on (-o, 0)? cx2 + 3x if x < 2 f(x) =…

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Q: Q4 A) What is the value of the limit of the function f(x) as x approach 0 x+2x-3 sinx + 4 <f(x) <…

A: Topic:- limits and function

Q: A tank contains 1720 L of pure water. Solution that contains 0.06 kg of sugar per liter enters the…

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: To find two path of approach for the given function such that we conclude that no limit exist when…

Q: Q3) if the continuous function is : 4x+1 F(x) -+k at x= h. Find the value of h,k.

A: 3). Given function is:   fx=4x+1x&lt;hx3+kx=hx2+1x&gt;h Solution: A function fx is continuous at x=h…

Q: The graph of f', the derivative of the function f, is shown below for the interval 0<xs10. The areas…

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Q: Find the limits. Are the functions continuous at the point being approached?

A: We will find the limit by substitution

Q: Calculate the limit x – y + 4vx – 4Vy Vx - Vy lim(x.y) → o(0,0) | Choose an option: a) -4 b) 0 c)…

A: Answer

Q: Compute the indicated values. If the value does not exist, type DNE. lim f(z) = x→5+ lim f(x) =|…

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Q: Estimate the limit by substituting smaller and smaller values of h. 6h lim- h-0 1 - Round your…

A: To evaluate:limh→06h-1h

Q: please answer parts a, b, and c

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given :               Whether the provided statement, "When the function y is differentiable,…

Q: Question: How else might you define "the limit as x approaches a of the function f (x) is L"? 3.

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Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: ) A tank contains 1700 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the…

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Q: Use the graph of the function f to find the limits at the indicated valu 4+ 3. y=f(x) 2 1 2 3 4 566…

A: Given query is to find indicated limit.

Q: (a) Is f continuous at the point (0,0)? Justify your answer. (b) Does the equality lim lim f(x, y) =…

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Q: Find the following from the graph of the function f(x) a) lim f(x)+ S(1) = b) Is the limit f(x)…

A: Graph of the function is given, we have to find its limit

Q: 8) Based on the graph of y = g(t) below, state the value of each limit if it exists. If it does not…

A: Observing from the given graph we have

Q: If f(x) is continuous at x=a, then a slope exists at x=a.

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Q: From the function H defined by sections a) Estimate the following limits: lim x→1/2h(x), lim…

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Q: The equation for the line tangent to f (x) at the point (7, 11) is given by y = 12x – 9. Use f(7+h)…

A: The equation of the line tangent is given by y=12x-9 Let ''m'' be the slope of tangent.…

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: Find the largest open interval using the tools of calculus where the function is changing as…

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Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

Q: 3. Is the function given by g(x) = x² x = 4? Why or why not? 3x continuous at

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Q: 5. Is the function given by F(x): = x = -1? Why or why not? Vx continuous at

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Q: Q2/Find the following limits for the function y= f(t) graphed below: -2 I- -る | @ lim, fCt) = %3D O…

A: See the attachment

Q: f(2) is continuos if lim f(z)=f(z)

A: continuity: A function f (z) is continuous at a point z0 if all three of the following are…