2 - x ifx < 1 f(x) = 1 if x = 1 if x >1

Q: Consider the function if g(x) = if 2. if x>0. And study its continuity at x=0

A:

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) = 3x2 - 2x + 1 a =…

A: Given, fx=3x2-2x+1 To determine whether the function f(x) is continuous at x=4

Q: Assume that a continuous function f:R → R is X- and µ-periodic, where A and u are two nonzero…

A: We know that between two rational number lies infinite many irrational number. But function is…

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

A: The denominator can not be 0.  So, x≠0 and x-1≠0  Or, x≠0 and x≠1

Q: (b) f(x) - (x + 2x')', a- -1

A:

Q: Determine if the function f below is continuous at x = 1: [1– VI– x, x 1

A: We have to find

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

A:

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x + 7)/(x - 7) a…

A: Given, f(x)= x+7x-7 and point a= 7 To determine: f is continuous at a Definition of continuity :  A…

Q: use the limit definition to compute f'(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. The…

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Suppose that f (x) &lt; 0 if x is positive and f (x) &gt; 1 if x is negative. Can f be continuous at…

A: f(x) will be continuous at x = 0 if LHL = f(0) = RHL

Q: Use the definition of continuity to determine whether f is continuous at a.

A: Given :           f(x) =  1 - x      if x &lt; 1             0           if x = 1            x2 - 1…

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x - 5)/(x + 5) a…

A: If the function is continuous at x=a then it must satisfy the conditions of continuity.  The value…

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x2 + 5x)/(x2 -…

A: The function is said to be continuous at the point at x=a it must be hold the following three…

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: Anwer: f'(0)=1

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*- x…

A:

Q: Use the definition of continuity to determine whether f is continuous at a.

A: f(0)=0-5=-5. limx→0- f(x)=limx→0- x-5=0-5=-5 limx→0+ f(x)=limx→0+ x2+x-5=02+0-5=-5

Q: use the Laws of Continuity and Theorems 2 and 3 to show that the function is continuous f (x) = ex…

A:

Q: f(x) = (x + 2x³)“, , a = -1 %3D

A: Limits Limit of the function at point a exists if and only if  left hand limit and right hand limit…

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (x) = x +…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. For a…

Q: Use the definition of continuity to determine whether f is continuous at a.

A: Solution:Given     f(x)=x-4if x≤0x2+x-4if x&gt;0and a=0To find :f is continuous at 'a'Formula:limx→a…

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: A function is continuous in an interval if is continuous on every point of the interval. Now, a…

Q: Use the definition of continuity to determine whether f is continuous at a.

A: Given: fx=x2-4x-2  if x≠25   if x=2 To Find:  To check whether the given function is continuous at…

Q: Use the definition of continuity to determine whether f is continuous at a.

A: To determine if a function is continous, it follows 3 conditions. The first condition is when the…

Q: 1. f(x) 2. f(x) = 3. f(x) x² - 4x X 2x x²-9 x² x-2 ; C = 0 -4 ; C = ; C = 2

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Use the definition of continuity to determine whether the shown function is continuous at a = 0.

A:

Q: Let f(x) = −2/x and g be the function defined b)Is f . g continuous at x = 3? If not, does…

A: limit of the composite function

Q: Cx) = *-2r+2 a-1 c = 2

A:

Q: and if the function is differentiable at x

A: The Given function is f(x)=x+33  ,  a=-3

Q: Use the definition of continuity to show that f is continuous at 2: f(x) = 3x2 – 2x + 1.

A: Definition of function continuity is: A function fx is said to be continuous at point x0 if and only…

Q: Use the definition for continuity to determine whether the function continuous at x= 1 and x= 2?

A:

Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

Q: Let f be a function that is continuous on the closed interval [1, 5] with f ( 1) = 10 and f (5) =…

A:

Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: f(x) = X-5 if xŹ 2 at x = 2 2x if x< 2

A:

Q: Use the definition of continuity to determine whether f(x) = 3x2 - 2x + 1 is continuous at a=4.

A: Given f(x)=3x2-2x+1we have to use the definition of continuity to determine the given functionis…

Q: Determine whether the statement is true or false. If f(x) is continuous at x = c, then so is f(x).…

A: Solution is given as below:

Q: Use the definition of continuity to show that h(x) = x^2 + 5x/2x + 1 is continuous at the number a…

A: The given function,   h(x)=x2+5x2x+1

Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

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: Let f (x) = xex . Use the limit definition to compute f ,(0), and find the equation of the tangent…

A:

Q: Use the definition of continuity to determine whether the given f is continuous at a =0.

A: the given f(x)=(x+3)2-9x        if x≠06                       if x=0 we have to use the definition…

Q: Use the definition of continuity to determine whether f(x) is continuous at a= 0.

A: Given function, We have to use the definition of continuity to determine whether f(x) is continuous…

Q: ) Use the Intermediate Value Theorem to show that there is one such that f"(a) = 0. point x = a

A: As per our guidelines we are supposed to answer only first 3 subparts of the question. Kindly repost…

Q: Use the definition of continuous to proce whether or not the function is continuous at x=5z (F2, D3)…

A: See the attachment

Q: f (x) = %3D x² +1

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.