c. Let f(x) = x > 2 is the f(x) is continuous at x=2. X-2 8, x< 2

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

A:

Q: Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)

A:

Q: 4. Is the function f(x) = (x + 1 ((x-4)² +3 ; x<4 continuous at x = 4? Why or why not? ; X24

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

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

A: Given function

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

A:

Q: If f is continuous on [a, b] and "If(x)| dx = 0, what can you conclude about f ?

A: Solution:Given If f is continuous on a,b and ∫abf(x) dx = 0To conclude about f ?

Q: ( 2x -. Is g(x) continuous at 2?

A:

Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

A: We are given : f(x)=x3       , x&lt;12Ax2     ,x≥12 is continuous at x=12 Condition for f(x) to be…

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: 3) Determine A and B that makes the function continuous as x approaches 0 and 1? y A x>1 x-B x<0

A: Given:           y=x2                  0≤x≤1A                   x&gt;1x-B             x&lt;0 Given…

Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: ecos-1 x if x 1

A: If a function has to be continuous  then it must to follow below Left hand limit = Right  hand limit…

Q: 10 If f is continuous and f(x) dx = -15, evaluate f(5x) dx. %3D

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: B) If f is differentiable at x, then prove that f is continuous at x Is the converse true? Why

A:

Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

A:

Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

A:

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

A:

Q: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

A:

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

A:

Q: (d) A function not continuous at 0 such that (f(x))4 is continuous at 0.

A:

Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: 9. If f is continuous and f(3x) dx. f(x) dx = 8, evaluate Answer:

A: Given:

Q: (x+1, l-x +1, x >0 Is f(x) continuous at x = 0? x30 Suppose f(x) =

A: We find the left-hand limit, right-hand limit and the value of f(x) at x=0

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

A:

Q: 10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

A:

Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: Where is f(x) = e* continuous?

A:

Q: Is f(x) = √x continuous at x = 0?

A:

Q: Let f be a continuous function such that 10 9 f(x) dx = 5. What is the value of f(x) dx = -6 and…

A:

Q: 4) Is the following functions continuous? for x < 1, d(x)= x- 2 for 1 < x.

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: 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: x3 B- If f(x) = ;, Find A? is continuous at x = %3D (Ax² x 2 1/N IN V

A: Given: f(x)=x3x&lt;12Ax2x≥12 Since f(x) is continuous at x=12. limx→12-f(x)=limx→12+f(x)

Q: 5. Is the function given by F(x): = x = -1? Why or why not? Vx continuous at

A:

Q: 1. Explain what it intuitively means for function f(x,y) to be continuous in some domain D.

A: To explain the meaning of the given statement.

Q: Show that x³, if x 0 is not continuous at x = 0. %3D

A: According to the problem, we have

Q: H.W Ex 2: Determine if the f(x) is continuous at x = 3 ? [x² – 1 f(x)=- |x² + 2 at x=3 at x+3

A:

Q: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

A:

Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

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

A:

Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

A:

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.