Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if x<2 O a. The function is discontinuous at x = 2. O b. The function is continuous at x = 2.

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: For what values of æ does the function f (x) = 12x – x³ have a horizontal tangent line? Select all…

A: We need to find the horizontal tangent line for: f(x) = 12x-x3

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

A:

Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: Determine if the given function below is continuous at x-2. Attached your complete solution and…

A: Topic = Continuity

Q: ] B1(a): Find the value of k that makes function continuous at x = 4 | 3x + 6 5х — k f(x) = x > 4 x…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: 19. Determine the following function if continuous at 2 f(x) = (,) ;at x = -1 + 1 A. discontinuous…

A: Explanation of the answer is as follows

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

A: We know that function is continuous only if its left hand and right hand limit equal, That is ,…

Q: - 3x + 1, x S 4 Find the value k , if the function ƒ (x) = is continuous at x = 4. -kx + 1, x > 4

A: We will find the value of k as following.

Q: Determine if the MVT applies to the function on the given interval. If so, find the points that are…

A:

Q: Consider the following function f(x) = - 3x? + 5x – 2 where r E (-, +0) Find the following: (a) The…

A:

Q: Use the given graph of the derivative f' of a continuous function f over the interval (0, 9) to find…

A: For any function, f(x), the sign of its first derivative, f'(x) changes from negative to positive…

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: Find the value of the constant (a , b, or c) that makes the function continuous.

A: the given function is: fx=x2-c          for x&lt;54x+2c      for x≥5 we have to find the value of c…

Q: Find the domain of the function. f(x) = √(ln x)

A: To find domain of the function fx=lnx. Solution: Domain is the input value for which a function is…

Q: Given the graph of derivative f'(x), find: a) Any interval(s) where f(x) is decreasing b) Any…

A:

Q: Consider the following function, where k is an unspecified constant. 28 + kx , x<3 f(x) = x< +x-k ,…

A: A given function is continuos everywhere, when the value of the function is sam on the breakpoints…

Q: B1(a): Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 6x – k x < 4 f(x) =…

A:

Q: For what values of a is the following function continuous for all x? Show the work. a²x +4a if x >…

A: See the attachment.

Q: Find the value of the constant & that makes the following function continuous on (-o, o). | 2x – 6…

A: fx=2x-6     if  x≤6-3x+b  if  x&gt;6 Since the function is a polynomial function for all x&lt;6…

Q: Find the inflection points of the function f(x) = ln(x^2 + 1)

A:

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

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

A:

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

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

A:

Q: Find the value for k so that the function will be continuous at x = 2. 4x + 16 if x 2

A: The function fx is continuous at x=a, if limx→a-fx=limx→a+fx It is given that fx=4x+16if…

Q: Determine if the given function is continuous at x=a and if the function is differentiable at x=a…

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

Q: For what values of k will the function below be continuous for all x? x³, xsk h(x) = x², x > k 1 and…

A: The function is said to be continuous at x=k if limx→k-f(x)=limx→k+f(x)=f(k).

Q: Find the constants "a" and "b" so that the following function sin 2x, if 0<xs. f(x) =- lax + b,…

A: Given f(x) is continuous and differentiable at x = π/6

Q: The graph of the derivativef'of a function f over the interval (a, b) is shown. y =f(x) (a) On what…

A: If f'x is positive then fx is increasing If  f'x is negative then fx is decreasing

Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: Make a graph of the functionƒ(x) , for x ≥ 1. Be sure to include all of the evidenceyou used to…

A: Given:  The function fx=∫1xdtt for x≥1, To sketch: The graph of fx for x≥1,

Q: Suppose that g: R →R is a differentiable function, with derivative g'(x)=(x – 1)·(x – 2)² - (x – 3)³…

A:

Q: Find the value of the constant cc that makes the following function continuous on (−∞,∞)(−∞,∞).…

A: We have been given a piecewise function and we need to determine the value of ‘c’ at which the given…

Q: Use f ′(x)=limh→0 f(x+h)−f(x)/h to find the derivative at x for the given function.   s(x)=8x+3 s…

A:

Q: Determine if the following functions grow faster, slower, or at the same rate as the function 4x as…

A: Given a function f(x)= 4x^2  Part a) To find the function grow faster slower or at the same rate as…

Q: (a). Determine whether the following function f(x) = -5z+6 when a 3 is continuous at x = 3. Justify…

A:

Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

A:

Q: For what value of the constant c is the function ff continuous on the interval (−∞,∞).

A: c=5 Answer and explanation is given below

Q: For any function f with continuous derivative f', are the following statements true of false? For a…

A: We have to check the given integration is true or not.

Q: Find the value of constant K that makes the function below continuous at x = 4. x2 - 4x X< 4 f(x) =…

A:

Q: Find the value of k so that the function defined by f(x) =kr - 15 S2² + 25 x 5 |-

A: Given that, The function defined by fx=x2+25x≤5kx-15x&gt;5 is continuous at x=5. To find the value…

Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A:

Q: Suppose ƒ is an even function and Evaluate

A: Given f is an even function, ∫-88f(x)dx=18

Q: The graph of f'(x), the derivative of a function f(x), is shown at right. Which of the following…

A: Use the concept of derivative of a function and check all the given options.

Q: x? + 2x + 1, if x 1. is continuous at x = 1 or not by using the definition of continuity.

A: f(x) = x2+2x+1  , if x≤14-x           , x &gt;1for a function to be continious at x = alimx→a+f(x) =…