x2 :- 4 if x + 2 f(x) = x – 2 5 if x = 2 a = 2

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) =(x2 + 6)/(x - 5) a…

A: A function f(x) is said to be continuous at a point x = a, if 1) f(a) exists. 2) limx→af(x)exists.…

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: 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: Use the definition of continuity to determine the value of the constant c for which the function f…

A:

Q: Consider f(x) = x6/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x-x3…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

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

A: Since, y=x is a continuous function Also, y= sin x is a continuous function

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

A: Given the function f(x)=(x2 + 4)/(x - 2) We need to use the definition of continuity to determine…

Q: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

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

A:

Q: Use the definition of continuity to determine whether the shown is continuous at a = 2.

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: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

A:

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: 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: 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: 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.

A: To check: Whether the function is continuous or not. Given: The function is fx=x2-9x+3 and a=-3.…

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: Find the values of a and b that make f continuous everywhere.

A:

Q: Investigate the continuity of the following function f(2)= if z +0 if z =0 (i) Is f(z)…

A: Calculate the limit:

Q: b. Test the continuity of the following function 1, V1-x,0sIs1, at x = 0,1 (x-2, x<0 x21

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 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: Let f: RR be a function satisfying f(x + y) = f(x) + f(y) for all x, ye R. If the function f(x) is…

A: Note :   Let r&gt;0 and c∈R ,then vr(c)={x∈R : x-c&lt;r }=(c-r ,c+r) ,which is called r…

Q: Determine a value of m (if possible) for which f is continuous at x = 4. mx – 48 if x<4 f(x) = 2 3x?…

A:

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: What values must a and b take for f to be continuous everywhere?

A: Given that the function fx=ax1+4x2 ,      x&lt;0b    ,                     x=0tan-1xx ,…

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

A:

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

A: Given function is

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 of continuity to determine whether f(x) = (x2 - 9)/(x + 3) is continuous at a=…

A: fx=x2-9x+3⇒fx=x-3x+3x+3 The common factor of numerator denominator is x+3. Therefore the given…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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

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: f(x) = 3x2 – 2x, -4+ x,

A:

Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4

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

A: Given function

Q: Use the definition of continuity to determine whether the shown function is continuous at a = 1.

A: Given:              fx=2-xIf x&lt;11If x=1x2If x&gt;1

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…

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.