10. Consider the following function. 1 x < -1 f(x) = ax + 6, -1 < x < } > } x > Find the values of a and b that make f(x) continuous. HIN

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

A:

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x² + 2x + 1…

A: Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: f(x) = at x = 1 X-2

A: A polynomial function is always Continous in its domain

Q: For what value(s) of x is the function f(x) = } 2x + 4 (x² +x +1 if – 2 sxs1 if x>1 NOT continuous?

A:

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: Are the following functions quasiconcave, quasiconvex, both, or neither: f(x) = x³ - 2x f(x₁, x₂) =…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

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

Q: 9. If f is continuous and 1| f(x)dx = 8, show that f takes on the value 4 at least once on the…

A: We need to show f takes value 4.

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

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

A:

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: On what domain is the function f(x)=1+√−6−3x continuous?

A:

Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

A: The given function is;  g(x)=13x+4for x≤32x-1, x&gt;3 we have to check the given function is…

Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

A:

Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: 10 if x c - everywhere then: С —

A:

Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

A:

Q: 35. Given that f(z) is a continuous even function, then A 0 B D

A:

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

A:

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: 45. For what value of the constant c is the function f continuous on (-∞, ∞)? Scx? + 2x if x 2

A: Let f(x)=cx2+2xif x&lt;2x3-cxif x≥2

Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

A:

Q: For what value of the constant c is the function f continuous on (-∞, +∞)? cz +4 if x ≤ 10 f(x) =…

A:

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x&gt;3 now show that it is continuous at x=3 or not.…

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

A:

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: 17.Determine the following function if continuous at p(x) = 3x? – x +5 ;at x = 1 A. discontinuous at…

A:

Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

A:

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x 4

A:

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: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

A:

Q: 4) Is the following functions continuous? for x < 1, d(x)= x- 2 for 1 < x.

A:

Q: . Is the function continuous on the interval (4, 10)? (x + 1 if x > 8 f(x) = E) + 7 if x < 8 A.…

A:

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

A:

Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

A:

Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

A:

Q: 3: determine whether following function are continuous ore not x² 4 f(x) X 2 x-2 4 X = 2

A:

Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

A:

Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for x 2…

A:

Q: Suppose that f (x) is a continuous function. 3 If | f(x) dx=5, then what is the value of z - f(x)]…

A: Given, ∫13f(x) dx =5Now,∫13[x -f(x)] dx= ∫13x dx -∫13f(x) dx =x2213 -5…

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

A:

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.