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

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: 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: (b) Test the continuity of the function f(x) = sgn(]x|) at x = 0. Is f(x) differentiable at x = 0?…

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Q: Let the function f(x) be defined by: 2x – 6 x + 3 f(x) = {Vx – 1– V2 2 x = 3 Determine the…

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Q: Let f(x) = V5x² – 20. Find everywhere f is continuous. -

A: Given fx=5x2-20

Q: Use the definition of continuity to determine whether f(x) = 2x + 5 at a = 1.

A: Given function is fx=2x+5.

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

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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…

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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: Suppose that f (x) < 0 if x is positive and f (x) > 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 < 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.

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.

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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: Determine the points of continuity of the function f (x) = x – [x] for all x E R.

A: Solution: The objective is to determine the continuity of the function f(x)=x-x for all x∈R

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: Show that Jx² + 2, x 1 is continuous but not differentiable at x = 1. Sketch the graph of f.

A: fx=x2+2,x≤1x+2,x>1

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = 2x2 +…

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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>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: Determine the points of continuity of the function f (x) [x] for all x E R.

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

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Q: Discuss the continuity of the function f(r) at a = 0.

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

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

A: Consider the given function as fx=x16-x2

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

A:

Q: Classify the statement as either true or false. If f is continuous at x= 2, then f(2) must exist,…

A: Given query is to find statement is true or false.

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: 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: 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: x 2

A: Consider the function f(x)=x-1              ,       x≤02x2-3x+1    ,       0&lt;x≤23x3-x2          ,…

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

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.