57. Find a constant b such that h is continuous at x = 2, where for |x| < 2 x+1 h(x) = |b – x? for |x| > 2 With this choice of b, find all points of discontinuity.

Q: Q2. Let f: R → R be a function such that f(x) = x sin f is defined at xo, where the value of 8…

A: We have to find the value of delta(d) in terms of x0 and e while evaluating the limit at x := x0 for…

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

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: 7. A function f (x) is continuous on the closed interval [2,5] withf (2) = 17 and f(5) = 17. Which…

A: Rolle's theorem

Q: Consider g(x) = x!/5. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: Given function

Q: 19. Determine the following function if continuous at 2 f(x) = (,) ;at x = -1 + 1 A. discontinuous…

A: Explanation of the answer is as follows

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

A:

Q: 46. Find the values of a and b that make ƒ continuous everywhere. 4 - if x < 2 f(x) = ax? if 2 <x <…

A:

Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

A:

Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: Find the x-values (if any) at which the functionf(x)= is not continuous. Which of the…

A:

Q: Determine the x-values (if any) at which f is not continuous and the type of discontinuity r+2 f (x)…

A: Solution is given below..

Q: Prove thait if y=f(x) f(x)=0 when x is a rotional number, then f(x)=0 for all x € R. is continuous…

A:

Q: Suppose f : R → R is a continuous function with the property that f(x) = 0 for every x E Q. Prove…

A:

Q: 45. For what value of the constant c is the function f continuous on (-∞, ∞)? Scx? + 2x if x 2

A: Let f(x)=cx2+2xif x&lt;2x3-cxif x≥2

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

A:

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

A: From the given problem: 57).   fx=12x+1,x≤23-x,x&gt;2   As we know that, if L.H.L is not equal to…

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

A:

Q: 4ex +x-k if x 0 be continuous everywhere?

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: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

A:

Q: 17.Determine the following function if continuous at p(x) = 3x? – x +5 ;at x = 1 A. discontinuous at…

A:

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

A:

Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

A:

Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: Find the constants "a" and "b" so that the following function sin 2x, if 0<xs. f(x) =- lax + b,…

A: Given f(x) is continuous and differentiable at x = π/6

Q: H.W Ex 2: Determine if the f(x) is continuous at x 3 ? at x-3 f(x) =- x²+2 at x 3

A: Given query is to find f(x) is continuous or not at x = 3.

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 4 10 8 5 5…

A: f(x) is continuous everywhere and has the following value: x 0 10 20 30 40 f(x) 4 10 8 5 5

Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

A:

Q: True or false 1. If the left- and right-hand limits of f(x) as x→ c exists and are equal,Then f(x)…

A: If f(x) be a function on a subset of real number and c be point in domain of f then f is continuous…

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

Q: 2x, ifx BDU G EDU y = 5, if x= 3 if x = 3 (x-5, if x 3

A: Given:   y=2xif x&lt;35if x=3x-5if x&gt;3 To prove whether y is continuous or not x=3. Solution: A…

Q: x²-1 for x# 1 - If flx) = show that flxx) is continuous at x = 1 x-1 2 for x = 1,

A: topic - limits and continuity

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: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

A:

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

A:

Q: (e) If f(x) is continuous at x = 0, then what is the value of n: if 20 if x=0 f(x)=\ 38

A:

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: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) - 2 7 10 - 4 7…

A:

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A:

Q: Find a constant b such that h is continuous at x = 2, where x +1 for |x| 2 With this choice of b,…

A: It is given that the continuous function  hx=x+1for x&lt;2b-x2for x≥2 It is also given that function…

Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

A:

Q: 22 + a For what value or values of k is f(x) = ka + 3k - 5 continuous at a = 5?

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point, take…

Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.

Q: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2