a) =ax - b, -1<

Q: a) Is f(x) continuous at x=2? Explain. b) What is the type of discontinuity of f(x)? c) On what open…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: We know,  ln(x) is continuous for all x&gt;0 Polynomial function of x is continuous for all real x.…

Q: Use the definition of continuity to determine the value of the constant c for which the function f…

A:

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

A:

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

A: Answer: False.

Q: If f' is continuous on [a, b], show that 2 f(x)f'(x) dx = (F(b))? – (F(a)² %3D -

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Q: Indicate whether the following statement is true or false. If f is continuous at a number, x, then f…

A: Solve the following

Q: For what values of a is

A:

Q: For what values of a and b is -2, f(x) = { ax – b, -1 <x< 1 3, continuous at every x?

A: Given: fx=-2,    x≤-1ax-b,    -1&lt;x&lt;13,   x≥1

Q: Is the function continuous on the interval 0, 27? 1+(sin z)? O yes O no cannot be determined

A:

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

A: Given: Lets consider the given, that Lft will not exist if f is not piecewise continuous on [0,…

Q: For what values of b is - b b + 1' g(x) x? + b, x > 0 continuous at every x?

A:

Q: If f(z) is continuous at z, then it must be differenttiable at z, ylgn O İhi O

A: If a function f(z) is continuous at z0 , then it may or may not be differentiable at z0. Hence, The…

Q: Suppose that ƒ is continuous on [a, b] and that c is an interior point of the interval. Show that if…

A: Mean Value Theorem:

Q: Prove that if f, g :R → R are continuous at x E R, then ƒ+gis continuous at x E R as well.

A: By using the definition of continuous function this above statement can be easily proved.

Q: Suppose that f is continuous at 0, and that f satisfies f(x + y) = f(x)+ f(y) for all real numbers…

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Q: Indicate whether the following statement is true or false. If f is differentiable at a number, x,…

A: Please refer the attached image for complete solution.

Q: Consider the function F(x) = | s(t) dt , where a is a constant and f is continuous everywhere. By…

A: Find we have to use definition of derivative.

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

A:

Q: Let f(x) = } sin , for # 0. Is f continuous at 0? Justify. Can f be defined at 0 so that it's…

A: A function f(x) is continuous at a point x=a if  fa-0=fa+0=fa

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: For what value of b is Sx, g(x) bx?, x 2 -2 X<-2 continuous at every x?

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

Q: Let f(x) = x?sin (-) for x + 0 and f(0) = 0. c) Show that f'is not continuous at x = 0.

A: Given function  f(x)=x2 sin1x      for x≠00                  for x=0 we have to show that f' is not…

Q: a) For which values of a and b in R is f(x) continuous on (-infinity, pi/2)? b) For which values of…

A: Given function is f(x)=x+a, x≤0bcos(x)+asin(x) , 0&lt;x≤π4btan(x), x≥π4 If f(x) is continuous on…

Q: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

A:

Q: O No, because f is not continuous on the closed interval [a, b].

A: Given that: The function f ( x) = x2 - 81x - 4     ,  [ -9, 9  ]  .

Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: Given f(z) = Arg(z+ 1), find all points at which f(2) is continuous. For a point of discontinuity,…

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Q: Let f, g : D → R be continuous at c E D. Prove that fg is continuous at c.

A: Let ε&lt;1 and M= maxf(a), g(a), 1, then there exists δ&gt;0 such that f(x)-f(a)&lt;ε3M (since f is…

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

A:

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

A:

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: Explain why, if f is continuous over [a, b], there is at least one point cin [a, b] such tha 1 f(c)…

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Q: Assume that ƒ is continuous on [a, b] and differentiable on (a, b). Also assume that ƒ(a) and ƒ(b)…

A: Given:                f is continuous on a, b and differentiable on (a, b)           Also, f(a) and…

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: 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…

A: 1/f is rational function this is discontinous where either f is discontinous or f is zero  But f is…

Q: Define h(0,0) in such a way that h is continuous at origin nu? – u?v? + nv?, h(u, v) = In(- u? + v?

A:

Q: If ƒ is continuous on [a, b] and, what can you conclude about ƒ?

A: the integral given to us is ∫ab|f(x)|dx=0

Q: Suppose f is continuous ont he closed interval [a, b). If F(x) is an antiderivative of f(x), for…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: B/ For what value of a is fo continuous at every x? x? – 1, x< 3 { fx) = 2ах, x2 3

A: Our objective is to find the value of a for which f(x) is continuous at every x.

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: If f(x) = is continuous at x=, Find A (Ar? Ax x2

A: Given: fx=x3,x&lt;12Ax2,x≥12 We know that any given functiony=fx is continuous at x=a If,…

Q: find the X-ualues (f ong at which f1s not Continuous, which of the discontinuities are removable?…

A:

Q: 1. Given that f is continuous on a, b|, compare f(b)(b – a) | f(x) dx, and if f is constant on a,…

A:

Q: Assume that ƒ is continuous on [a, b] and differentiable on (a, b). Also assume that ƒ(a) and ƒ(b)…

A: According to the given information: Assume that ƒ is continuous on [a, b] and differentiable on (a,…

Q: If f(x) is continuous with f(a)f(b) < 0, then the e Select one: O an indeterminable number of roots…

A:

Q: If f is continuous on R, prove that For the case where f(x) = 0 and 0 < a < b, draw a dia- gram to…

A: A function is said to be continuous if for all the real values, the function is defined.

Q: Assume that ƒ is differentiable on a&lt;=x&lt;=b and that ƒ(b)&lt;ƒ(a). Show that ƒ′ is negative at…

A: Given,

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.