4. Determine if 1 1 sec if – 1< x < 0 f(x) = [Зл — 2] + х if 0 < x <1 |x2 – 3x + 2| if x > 1 x – 1 is continuous or not at x = 0 and 1. In the case of discontinuity, identify the type

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: (0,1). Prove the following functions is uniformly continuous on sin x f(x) =

A: Uniformly Continuous:-  Here we prove the result using a theorem of uniformly continuous.

Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

A:

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

A: Given function

Q: 17. Show that f(x) = x² +2x is uniformly continuous on the interval [0, 10], using the e -8…

A:

Q: Suppose that h(x) has a continuous derivative h'(x), h(0) = -2, h(T/4) = 2 and tan(x)h'(x) dx = 4.…

A:

Q: Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]

A:

Q: 2. (a) Suppose that f is a differentiable function such that |f'(x)| < c for every x. Show that for…

A: To Prove: a. If f is a differentiable function such that f'(x)≤c for every x.Then for any real…

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: 21. Discuss the continuity of : 1 for x+- x 2 (ans.: discontinuous at x=0,2 ; continuous at x=1)

A: Given: f(x)=x+1x   for x&lt;0-x3      for 0≤x&lt;1-1       for 1≤x&lt;21          for  x=20…

Q: 1- Discuss the continuity of the following functions at given poin { V9r4+x² 5x2+3x+1 (a) f(x) = if…

A: It is given that

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: 1- Discuss the continuity of the following functions at given points { V9r4+x² 5x2+3x+1 ,if a 0 (a)…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: Show that g(x) = (x3-8) / (x-2) has a removable discontinuity at x = 2. How should g(2) be defined…

A: The left-hand limit of a function at a point is the value of the function at a point very close from…

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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: 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: 1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2…

A:

Q: 4. Find the first two intervals using the bisection method to compute the minimum of the function…

A: We need to find the first two intervals of on the interval

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A: Given: f'(1)=f'(3)=0 f'(2) is undefined. f has an absolute maximum at x=2, f has neither maximum nor…

Q: 2 cot- (ecsc) if – 3 3. - a. Determine if f is continuous or discontinuous at x= continuous,…

A:

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

A:

Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

A:

Q: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: Assume that ƒ is continuous on [0,1] and that f(0) = 2 and f(1) = 1. Show that the graph of y = f(x)…

A: given  f is continuous on [0,1] f0=2,f1=1y=x2+1

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

A:

Q: Let fc Cx)= Vx if osxs 4 c.(x-4)+2 if x>4 denotes a real constant. - where C Show that lim fe (x) =…

A: The function fcx=x,              if 0≤x≤4cx-4+2   if x&gt;4. Where c is a real constant. We have to…

Q: 2. Determine whether f is continuous or discontinuous at 1. (x – 1 if x > 1 f(x) -x² if x <1 O f is…

A: Given query is to find function is continuous or not at x = 1.

Q: [2x – 5] x if 0 3. - Determine if f is continuous or discontinuous at x = 0 and at x = 3. If di…

A:

Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

A:

Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

A:

Q: 3. Use the MVT to show that the function f(x) = 1/x³ is uniformly continuous on the interval 3,00).…

A:

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: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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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: A function ƒ is continuous for all x and has a local minimum at (2, –5). W statement below must be…

A:

Q: 13. Let g be defined by V7x +2 V6x + 4 | g(x) = if x 2 - and x 2 x – 2 k , if x = 2 For what value…

A: The given functiong(x)=7x+2-6x+4x-2,if x≥-27 and x≠2k,if x=2

Q: Suppose f '' is continuous on (−∞, ∞). (a)  If f '(−3) = 0 and f ''(−3) = 7,  what can you say about…

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Q: 2.23 Let 1 - x2 f(x): if x € Q, if r ¢ Q. Find all points p at which f is continuous. Prove your…

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

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Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &amp;  f"(x)=12x2

Q: If f is positive-valued continuous decreasing function and lim - S(x) = 0 then J F(x)dx diverges…

A:

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

A: