Use the intermediate value theorem to explain why the function f(x) = x2 - 4 must have at least one zero in the interval (-5,-1) 5. Use the following graph of the function to answer the following questions. 6. HA yfix) Determine all point of discontinuity. At each point of discontinuity, state the condition for continuity that is violated. Determine the values of x where f (x) is not differentiable. State why each value is not differentiable. What is the equation of the tangent line of f(x) x2-x + 2 at x = 3? 7.

Q: Test the continuity of the following functions at the indicated points of each x < 1 (1) f(x) = { 3x…

A:

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: Determine if the following function is continuous at x = 4. Show all steps by definition of…

A: This question is based on Continuity of function.

Q: Use the definition of continuity to determine whether the shown is continuous at a = 2.

A:

Q: Consider the following. -9x, f(x)=2 - 2x + 7, x > 6 Find the x-value at which f is not continuous.…

A: Givenf(x)=-9x ,   x≤6x2-2x+7  , x&gt;6The function is continuous ifLHL=RHL =f(a)ie limx→a-…

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

A:

Q: Use the definition of continuity and the properties oflimits to show that the function is continuous…

A:

Q: Use the definition of continuity to decide if the following function is continuous at a = -1. -1.0x²…

A:

Q: Given the function, g(x) 3 x 2 a. Determine the possible points of discontinuity. b. Discuss the…

A:

Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

Q: b. Test the continuity of the following function 1, V1-x,0sIs1, at x = 0,1 (x-2, x<0 x21

A:

Q: Determine the set of x-values where y = x - 4 r2 +9r+18 is continuous, using interval notation.

A:

Q: (x – 2)2 +1 if x 2

A: We have to check continuity of function at x=0 and x=2

Q: 1. Consider the function 4.x + 8 { if x 0 Use the definition of continuity to determine all the…

A:

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*- x…

A:

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: please answer the two questions that are part of 6's graph. thank you

A: To discuss the continuity and diiferentiablity of the  function (from the graph)

Q: Use the definition of continuity to determine whether f is continuous at a.

A: To determine if a function is continous, it follows 3 conditions. The first condition is when the…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: 1. f(x) 2. f(x) = 3. f(x) x² - 4x X 2x x²-9 x² x-2 ; C = 0 -4 ; C = ; C = 2

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

A:

Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

A:

Q: Use the definition of continuity to show that f is continuous at 2: f(x) = 3x2 – 2x + 1.

A: Definition of function continuity is: A function fx is said to be continuous at point x0 if and only…

Q: Use the definition of continuity to determine where f(x) is continuous. If it's discontinuous point,…

A: We will solve the problem

Q: Consider the function defined by f(x) = -(x + 1)² +5 if x 4 Graph the function. Is the function…

A:

Q: Give the three conditions that must be satisfied by a function to be continuous at a point.

A: We have to write  the three conditions that must be satisfied by a function to be continuous at a…

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*x…

A: Let's find.

Q: ((4— х)2 х 1 continuity at the indicated test point. If it is discontinuous, specify the type of…

A:

Q: The function whose graph is given below is discontinuous at x = 1 because the third condition of…

A: A function f(x) is continuous at a point c  if and only if the following three conditions are…

Q: Use the definition of continuity and the properties oflimits to show that the function…

A: Consider the given function as fx=x16-x2

Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

A:

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

Q: Q2/B/ check the function continuity at x-0, for the fimction f(x)%= 1+ 4 2/3

A:

Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

A:

Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: f(x) = X-5 if xŹ 2 at x = 2 2x if x< 2

A:

Q: b) Discuss the continuity conditions of the function- f(x) which shown in figure at x= 0,x = 1,x= 2…

A:

Q: Use the definition of continuity to determine whether f(x) = 3x2 - 2x + 1 is continuous at a=4.

A: Given f(x)=3x2-2x+1we have to use the definition of continuity to determine the given functionis…

Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4

Q: What type of discontinuity is present in the function 3x – 2 if r 2 O The function has a removable…

A:

Q: Graph the function

A:

Q: Use the definition of continuity to determine whether the shown function is continuous at a = 1.

A: Given:              fx=2-xIf x&lt;11If x=1x2If x&gt;1

Q: Consider the following figure. y f(x) whether the function is continuous or discontinuous at that…

A: Given query is to check the characteristics of function for x = -2.

Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

Q: Q12: Discuss the continuity of function f(x) at x-3 x²-9 if x # 3 6 if x = 3 F(x) = {x-3 %3D

A:

Q: Use the definition of continuity to determine whether f(x) is continuous at a= 0.

A: Given function, We have to use the definition of continuity to determine whether f(x) is continuous…

Q: The function whose graph is given below is discontinuous at x = 1 because the third condition of…

A: We can answer the question as below