If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: -x²+5 < f (x) < x+1 2

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Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x&gt;5 We have to find the value…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

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

A:

Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: (b). Show whether (*) is continuous at *=-2, if (3x-2 for x = -2 S(x)=. x? - 4 х- 2 for x * -2

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Q: 3x+8x74 F(x)=(7x-K x<4 X=4 11

A: Given f is continuous at x=4

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Give an example of a function that is continuous but differentiable at x=2

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Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

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: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

Q: 10 if x c - everywhere then: С —

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

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Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: for x 1 x -1 = ( JI- 2 for x = 1, show that flx) is continuous at x = 1

A: If fx=x2-1x-1  for x≠12  for x=1then to show that fx is continuous at x=1.

Q: Find the value for k so that the function will be continuous at x = 1. - 5x2 - 30x + 35 - 10 if x <…

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Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 When is the function concave up and concave down in…

A: For concavity we need second derivative.

Q: find f'(x) for f(x) = 2xtan-1 x - ln(1+x2)

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Q: What is the domain of g(x)=ln(25x-x^2) Show all the work.

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Q: Show that x+1/x is increasing on [1,∞]

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Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

A: A function is a relation from a set of inputs to a set of possible outputs where each input is…

Q: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

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Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: If 5х + 3,х <2 { h(x) = 2x2 + 5,2 < x < 4 Is h(x) continuous at (x=2)?

A: We use definition of contunity

Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: x²-a if x2 is continuous at x-2, then x+3 if x-2 If the function fo)

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Q: f(x)=√√x at x = 7

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Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

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Q: x² - 2x-8 if x+ 4 (4) F(x) =, x-4 if f is continuous at x=4, а, if x = 4 then a =.

A: Topic:- limit and continuity

Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

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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.