Determine the discontinuities of the following functions and state why the function fails to be continuous at those points: x2-3х-10 (i) F(x) : х+2 х4—1 (ii) F(x) = x²-1

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

A: A polynomial function is always Continous in its domain

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

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Q: the function f is not differentiable at x=0.

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Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

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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: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

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

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

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: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: f(x): at x = 3 X-3 f(x) = at x = 0 f(x)%3D%x6 at x - 0

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

A: Given       y = ln(x + 7)

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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

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Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: Evaluate f (x): at x = -2. %D 1 - x2 Select one: A. Discontinuous B. Continuous

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Q: f(x) = Vx-3

A: Given function is fx=x-3.

Q: f(x): 2x at x = 4 x2-3 f(x) = V3x - 10 at x = 2

A: According to question,a. Given function,fx = 2xx2 - 3

Q: Is the function given by f(x) = 5X+6, for x s5, 5x-14, for x>5, continuous at x=5? Why or why not?

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Q: Show that the function is discontinuous on R. f(x) = { 1; 0; for x € Q for a Q

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Q: Find the value for k so that the function will be continuous at x = 1. - 5x2 - 30x + 35 - 10 if x <…

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Q: Find a function f such that f'(x) = x4 and the line 2x - y = 3 is tangent to the graph of f.

A: Given that

Q: Find the interval(s) where f(x)= x²- 2x+3 is continuous.

A:

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: Let f(x) = V5x + 2. Find the derivative f'(x) using the limit definition.

A: We have to find derivative

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

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Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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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 a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

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Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

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: Find the values that make the piecewise function continuous: 2, XS-1 f(x) = ax + b, -1<x< 3 x2 3 -2,

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Q: Find the value k that makes the function continuous. Ska², f (æ) = x > 2 kx + 12, x < 2

A: Topic - continuity Function is continuous If its left hand linit is equal to right hand limit and…

Q: Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Determine whether the following function is continuous at the given point z= 22 +9z – 5 f(=) = 2x-1…

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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: Show whether the following function is continuously differentiable: f(x,y)=x2y2

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Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

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.