Let f be defined as follows: Sx+5 for x> 5, f(x) = Зах for x <5 } For what value of a is the function continuous

Q: Describe the interval(s) on which the function f(x) = is continuous.

A: The given function fx=xx2+x+2 is in gxhxform. The numerator gx=x is continuous for all x∈-∞,∞ in its…

Q: 1 f(x) rank- 3x

A: Let's find.

Q: Determine whether function is continuous and/or differentiable at x = 1. f (x) = 1/x

A: Consider the given function fx=1x

Q: Describe the interval(s) on which the function is continuous. f(x) = 3 − √x

A: Given function is

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: is the function f(x) = 1/(x-2) continuous on [1,3]? Justify your answer.

A:

Q: Define f(x) = (x2 - 81)/(x - 9) at x = 9 so that the function becomes continuous at 9.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Define f(x) =(x2 - 81)/(x - 9)at x = 9 so that the function becomes continuous at 9.

A: Given function is fx=x2-81x-9. To define function fxso that the function becomes continuous at x=9.…

Q: Let f be defined as follows: x2 +5 for x > 5, Зах f(x)3D for xs5 For what value of a is the function…

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Q: nuous

A: The function f is continuous at some point c of its domain if the limit of f(x), as x approaches c…

Q: Describe the interval(s) on which the function is continuous.

A: Given: Describe the interval(s) on which the function is continuous. f(x)=sec πx4Clearly from the…

Q: What conditions must be satisfied by a function if it is to be continuous at an interior point of…

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Q: Let f be the function defined by: sin x, x <0 x2, 0 <x < 1 2 - x, 1<x < 2 x-3, x22 f(x) = %3D For…

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Q: Find the number c which will make the function continuous on (-00, 00). x< 2 f(x) = x+ c, x22

A:

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: Determine where the function f(x) is continuous.

A: The given function is , fx =x-8

Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

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Q: Determine if the function is continuous at the given point. Sx³ x 2) f(x) = at x = 2.

A:

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1&lt;x2 then fx1&gt;fx2 claim- is it decreasing or increasing

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

A:

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: suppose that f is a function satisfy |f(x)|&lt;=|x| for all x. Show that f is continuous at f = 0.…

A: Suppose that there is a function f that satisfies

Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: To prove that given function is continuous. gx,y=xy3x2+y6,   if x,y≠0,00,              if x,y=0,0

Q: Is the function given by f(x) = 5X+6, for x s5, 5x-14, for x>5, continuous at x=5? Why or why not?

A:

Q: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

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Q: Is the function given by f(x)=x^2+3x/2x-1 continuous over its domain?

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Q: Determine algebraically if f is continuous at x= 0.

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Q: Let f be a function of multiplicity 5 at P. Then at P, µ(x) f(x) has multiplicity: f(x)'

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Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

A:

Q: Where is f(a) not continuous?

A: Given:

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: Determined where the function f(x) is continuous

A:

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

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Q: Find the value of a and b that will make the function continuous. for x 1/2

A: The function f(x)=1x,        for x&lt;-1ax+b,  for  -1≤x≤121x,         for x&gt;12. We have to find…

Q: Find the value k that makes the function continuous. Ska², f (æ) = x > 2 kx + 12, x < 2

A: Topic - continuity Function is continuous If its left hand linit is equal to right hand limit and…

Q: Determine the set of points at which the function is continuous

A: f (x, y, z) = sin-1 (x2 + y2 + z2) = t (Let's say)Hence, sin t = (x2 + y2 + z2)

Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

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: Determine at which points, the function 97× ナ x²if x E RIQ f(x)= is continuous.

A:

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

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.