2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at x= 3.

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

A:

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

A:

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: Use the given derivative to find all critical points off, and at each critical point determine…

A:

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

A: Given function

Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

A:

Q: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

A:

Q: 19. Determine the following function if continuous at 2 f(x) = (,) ;at x = -1 + 1 A. discontinuous…

A: Explanation of the answer is as follows

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

A:

Q: 1. What is the definition of what it means for f(x) to be continuous at x = a? Discuss the ways that…

A: In this question, we need to define the meaning of f(x) to be continuous at x=a and different ways…

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)>0 then function increasing when f'(x)<0 then function decreasing

Q: 3. Define the function sin(2x – 2) x 3 3' - Determine if f is continuous at x = 1 and x = 3. If…

A:

Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

A:

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

A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

A:

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: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: Use the given derivative to find all critical points off, and at each critical point determine…

A:

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

A:

Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

A:

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

A:

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

A:

Q: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

A:

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

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

A:

Q: If a function f(x) is not defined at x-a, then it is not continuous at x-a.

A:

Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

Q: 4x-8 i- -2 x +3a

A:

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

A:

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

A:

Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

A:

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

A:

Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

Q: Suppose f is differentiable with f(0) = 0 and 0 0.

A:

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

A: According to the problem, we have

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: 5) Show that the function f(x)=-÷+1 below is continuous at x = -1. x-1 2- -3 -1- -2 1.

A: A function f(x) is continuous at x=c if  We have to show that is continuous at x=-1.

Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

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

A: we have to find the value of given function. the solution is following.