For the following exercises, decide if the function continuous at the given point. If it is discontinuous, what type of discontinuity is it? 139.  f(x) = 2x^2 − 5x + 3 / x − 1 at x=1

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: Find the most general antiderivative of the function. (Chec values where appropriate.) Write your…

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

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Q: 50. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Given: fx=3x-2 Concept Used: Linear function is continuous everywhere.

Q: Use the definition of derivative to find f'(x) for f(x) = ax² + 10. f(x+h)– f(x) | f'(x) = lim h0 h

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Q: 4x -5x-6 for x +2 Given f(x) 2-V2x 4 for x = 2 Is the function f continuous at x = 2 ? Give…

A: A function f(x) is continuous at x = a if limx→a+f(x)=limx→a-f(x)=limx→af(x).

Q: For the following exercises, use the second derivative test to identify any critical points and…

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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: 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: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

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: How would taking a reciprocal of a function f (i.e., 1/f) affect its elasticity? Assume f is…

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Q: x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

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Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: Find the average rate of change of the following functions as a function of Δx, and find the limit…

A: Please refer to the image below

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

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Q: y=x²-3x²-9x +4

A: The given function is y=x3-3x2-9x+4

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: To find two path of approach for the given function such that we conclude that no limit exist when…

Q: where is the function f(x)= llxll-2 continuous (or discontinuous)?

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Q: The graph of f', the derivative of the function f, is shown below for the interval 0<xs10. The areas…

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Q: For the following exercises, decide if the function continuous at the given point. If it is…

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Q: 0>x x_} = (x)/ at x = 0 j(x) = { %, x20

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Q: The height of an arch above the ground is given by the function y=10sinx, for 0 less than or equal…

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Q: Calculate the extremum point of below function and Classify it f(x) = 4 x³ + 2 v11 – x + x?

A: It is given that fx=4x3+211-x+x2. We have to find the local maximum and local minimum points of the…

Q: Find the x-values at which f is differentiable. (Enter your answer using interval notation.)

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Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

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Q: For what value of the constant c is the function f continuous on (-∞, 0)? if x 5 C = Need Help?…

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Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

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Q: In our last class discussion we found that a function y(x)= x* indicated by taking y"(x) = 0 that…

A: Definition: The first derivative of a one-variable function is zero at the points called stationary…

Q: find the value of c that make the function continuous

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Q: The sales of a book publication are expected to grow according to the function S= 300000(1−e−0.06t),…

A: It is given that sales of a book publication are expected to grow according to the function…

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: Find the value of a and b that will make the function continuous. for x 1/2

A: The function f(x)=1x,        for x&lt;-1ax+b,  for  -1≤x≤121x,         for x&gt;12. We have to find…

Q: 4. For each part, find a real value c that makes f continuous at x=0, if possible. If not possible,…

A: A function is continious , when at that point limit of the function exists , and thatlimit is equal…

Q: Given the graph below, what can you say about the function at x = -1? Continuous Not Continuous

A: Explanation of the answer is as follows

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

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

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Q: For the following exercises, use the limit definition of derivative to show that the derivative does…

A: To find the derivative of a function by using the definition of a limit, fx=x2x2+1 at x=a, let f:…

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: Find a formula for a function that has vertical asymptotes x =1 and  x = 3and horizontal asymptote y…

A: Given that a function has vertical asymptotes x=1 and x=3 and horizontal asymptote is y=1. To find…

Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

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Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Find all points where the function f(x)=|x|^p is differentiable. How does the answer depend on the…

A: The left-hand derivative of the function at x=a is given by the expression…

Q: x' - 8 24. f(x) : x? – 4

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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.