Use the definition to determine whether the following function is continuous and differentiable at x = 2.  f(x) = x − 1 for 0 ≤ x < 2 1 for x = 2 2x − 3 for x > 2

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: Determine the value for k that will make the function continuous at c = 4. x² – 9 if x 4

A: Left-handed limit of a function at a point is obtained by approaching the point from the left on the…

Q: What are the values of a and b that make f(x)=ax+a+b+1  x>0 continuous and differentiable

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Q: Is the function g(x) continuous at x = 5? g(x)= O No 1 5X+7, 5x-13, for x>5 Choose the correct…

A: Given query is to find function is continuous or not at x = 5.

Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a.…

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

A: If function is continuous  Then, it will be continuous on x=-1 and x=12 Therefore, limx→-1-1fx=f-1…

Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

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: is the function f(x) = 1/(x-2) continuous on [1,3]? Justify your answer.

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Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for 5≤x≤5 f(x) = 2x…

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Q: f(x)% = x- 3x3 + 2x2-5x-7 at x = -1 %3D vnaud

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Q: Is the following function continuous? [x² + y² _if x² + y² ! f (x, y) =

A: The left-side limit, the right-side limit, and the value of the function at that point can be…

Q: Determine if the following functions are continuous at the given value of x. Show your solution. 1.…

A: A function f(x) is continuous at x=c if the left hand limit, right hand limit and the value of the…

Q: Evaluate and tell whether the given function is continuous or not. 1. f(x)=Vx+ 3 at x=3 2. f(x)= x-9…

A: Let's Solve,

Q: Find the value a that will make f(x)={2x^2-7x+3/x-3  if x is not equal to 3…

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Q: 3) Determine A and B that makes the function continuous as x approaches 0 and 1? y A x>1 x-B x<0

A: Given:           y=x2                  0≤x≤1A                   x&gt;1x-B             x&lt;0 Given…

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

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

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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: Consider the function f(x) : Find the value of B such that (3x + B if x> 3* f(x) is continuous at x…

A: Given: fx=2x2+3  if x≤33x+B   if x&gt;3

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

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Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

Q: (x – 2)2 +1 if x 2

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

Q: Determine if the following are continuous at the certain point. Show your | COMPLETE SOLUTION. f(2)…

A: Authoring guidelines: As per the authoring guidelines we can solve only the first three parts of…

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: Let f(x) | x? + 4x – 5 if x > – 6 - If f(x) is a function which is continuous everywhere, then we…

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Q: Determine if the piecewise function is continuous at a. x-3 x + 3 f(x) = 1, x-3 a = 3 x = 3 O Yes,…

A: Topic- limit

Q: Determine if the following functions are continuous at the given value of x. Show your solutions. 1.…

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Q: Describe the interval(s) on which the function is continuous.                            f(x) =…

A: fx=xx2+x+2 Since there is no common factors in the numerator and denominator, therefore there is no…

Q: Determine the values of a and b such that the function is continuous on (-00, oo f(x)-ax+b, -l<x<3…

A: We have to find value of a and b so that function is continous is given interval  (-inf,inf)Function…

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: For what value of k will the function f be continuous on (-0,0)? x² –100 f (x) = { * if x + -10 =…

A: Continuous function should not have any abrupt (sudden) changes.

Q: B- If f(x) = is continuous at x = Find A? |Ax2 x2

A: The explanation of the answer as follows

Q: Determine whether the function f(x)=5+3x if x <4…

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Q: Determine whether the function is continuous at the given points. x+30 if x26 6, 0 if x <6 f(x) = Is…

A: Solution

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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Q: f(x) = 2x² – x + 6 for all values of x %D

A: Given function is, f(x)=2x2-x+6

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

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

Q: Determine if the function is continuous or discontinuous at x=2. h(x) = x - 1, if x 22 2x- 1, if x<2…

A: if Left hand limit and right hand limit are equal then function is…

Q: Determine if the following functions are continuous at the given value of x. Show your solution. 1.…

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Q: 4. Determine the possible pairs of values (a, b) which make the function below continuous…

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

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Q: Find the values of a and b that make f continuous everywhere x2 4 - if x 3 a %3D b =

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Q: Determine the discontinuities of the following functions and state why the function fails to be…

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Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

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Q: What values of a and b will make the function f continuous at x=2 and x=3? * x2 - 4 if x 3 2x – a…

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Q: Is the following function continuous at r= 5? Explain your answer. 5x if r 5

A: Given  f(x) = 5xif x&lt;512if x=5x2if x&gt;5 We have to check the continuity at x=5.

Q: On what domain is the function f(x) = 5+ V2x + 6 continuous? %3D

A: Let's find.

Q: Find the values of a and b such that the following p Function is continuous at points -2 and x-5…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: