1 - is continuous at a. f If f(x) 0 for all x in the interval I, and f is continuous at a in I then Select one: a. False b. True

Q: If f is differentiable at a, then f is continuous at a.

A: If a function fx is differentiable at x=a then function must be continuous at x=a. But a function…

Q: Find the x-values (if any) at which f (x)= 1s not continuous. x²+ 3x O fx) is not continuous at x =…

A: It is known that to check the continuity, we can equate the denominator part with 0.   Here, we…

Q: 4. h(x) = x-T at X %3D 2. 5h(X) = x + x4-1 at X = %3D

A: Continuous function at x=a

Q: If f is continuous but not differentiable at x = c then there is a corner on its graph at (c, f(c)).…

A:

Q: Answer true or false. If f is not piecewise continuous on  [0, ∞>),  then  ℒ{f(t)}  will not exist.

A: Given problem:- If f is not piecewise continuous on [0, ∞),then ℒ{f(t)} will not exist.  True…

Q: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: It is given that,  g : a, b → ℝ is continuous and F is a function defined as ;  F(x) = 1,x∈a,…

Q: If f is differentiable at a number, x, then f is continuous at x.

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Q: If f(x) is continuous in the interval [-2, 1], ƒ(−2) = −4, and f(1) = -1, can we use the…

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Q: Suppose that ƒ is continuous in [0,1] and that f(x) E [0, 1] for all x. Show that f(x) = x for some…

A: Given that f:0,1→0,1 is continuous on 0,1. To show fx=x for some x∈0,1

Q: Suppose that the function f: [0, 1] in R is continuous, f(O) > 0, and f(l) = 0.Prove that there…

A:

Q: Find a value of x, if any, at which f (x) = Vx – 125 is not continuous. If f(x) is continuous for…

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Q: Suppose f is continuous on the closed interval [- 1, 3]. If Fis an antiderivative of f , which of…

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Q: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: Please comment if you need any clarification. If you find my answer is useful please put thumbs up.…

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

Q: 5) Suppose that f is continuous on (-00, 00). How many non-differentiable points could f have? Is it…

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Q: If a function f(x) is not defined at x-z, then it is not continuous at interval (a, b) where a > z <…

A: Solution

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then L{f(t)} will not exist. O…

A:

Q: Assume f(x) is continuous on [a, b]. Prove that if f(x) > 0 for all x € [a, b], then S. f(x) dx > 0.…

A: Extreme Value theorem states that if a real-valued function f is continuous on the closed inteval…

Q: If a function f is not defined at x = a then it is not continuous at x = a. Select one: O True O…

A: As we know that a function f(x) is said to be continuous at x=a when the right-hand limit and…

Q: Suppose f " is continuous on (-o, ). (a) If f '(1) = 0 and f "(1) = -7, what can you say about f? O…

A: Consider the given information.

Q: Suppose f  is differentiable on an interval I and f'(x) &gt;0for all numbers x in  I except for a…

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Q: 2- For what value of the costant c is the function continuous at every number? F(x) = {x+c if x<2…

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Q: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

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Q: If a function f(x) is not defined at x-a, then it is not continuous at an open interval (a, b) * O…

A: Given Statement is "False"

Q: 7. Show that if f is differentiable on (a, b), and f'(c) > 0, where ce (a, b) and if f' is…

A:

Q: 16.C. If f is defined and continuous on R? to R and if f(xo) > 0, then is f positive on some…

A: Consider the provided question,   We need to show that, f is strictly positive on some neighborhood…

Q: Let f(x) = −2/x and g be the function defined b)Is f . g continuous at x = 3? If not, does…

A: limit of the composite function

Q: Suppose f is continuous on [a, b], ƒ'(x) exists at some point x e [a, b], g is defined on an…

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Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

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Q: iii If the discontinuity of ƒ is removable, redefine ƒ so that it's continuous at 0

A: This question related to the topic continuity of real analysis.

Q: Suppose f is continuous on the closed interval [a.b]. If Fis an antiderivative of f for all real…

A:

Q: If f is continuous on [a, b] and f(x) 20 for all x E[a, b], then Select one: O True O False

A: Let f(x)=x, x∈2, 3 I=∫23f(x) dx =∫23xdx =x323223 =23x3223 =23332-232 =2333-22

Q: Consider g(x) = rº/3. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: We find g'(x) using the power rule  Then we find the left and right-hand limits of g'(x) and g'(0)…

Q: If X is continuous on the interval 0 to 10, t O True False

A: For a continuous distribution, and there exist infinite points.

Q: 3. Suppose f is continuous on an open interval containing x, and f has relative extremum at x = x,…

A: The solution is :

Q: On which of the following interval is f(x) S O (0, +∞0) ○ (2, +∞) O [2, +∞0) 0 (-∞, +∞0) 1 x-2…

A: We will the fact that root value should be positive.

Q: 3. For what value of b, f(x) is continuous at every x? f(x) = {, x -2

A: Given that, fx=x         x&lt;-2bx2      x≥-2

Q: For every continuous function f(x) defined on symmetric interval [a,b]. If f(x) is an even function…

A: Here, the given function f(x) is even. So, f(-x)=f(x)

Q: Suppose f is continuous on the closed interval [–1,3]. If F is an antiderivative of f, which of the…

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Q: If f(x) is a continuous function such that it is increasing on [1, 3], then Si f(x)dæ is less than…

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Q: Suppose that f is continuous on [a.b] that f(x) 20 for all xE[a,b] and that f =0 1. Prove that f(x)…

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

Q: ) For a, 3 ER and B > 0, let f(x) ={} x° sin(|x|-#), when x # 0 when x = 0 0, ange of a and B (and…

A: Continuity and differentiability

Q: If f(x) is continuous on a closed interval I, and f(a) and f (b) have opposite signs where a and b…

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Q: 3. Consider the function f(x) : (0, 00) → R where f(x) = . (1) Show by definition that f is…

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Q: 18.Q. Is it true that function on R? to R is continuous at a point if and only if it is both upper…

A: exercise 18.Q

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.