Consider the following. PX)={ S-5x, f(x)= x² – 2x + 5, X < 4 X > 4 Find the x-value at which f is not continuous. Is the discontinuity removable? X = ; nonremovable

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist.…

A: The given statement is

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

A: We know,  ln(x) is continuous for all x&gt;0 Polynomial function of x is continuous for all real x.…

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

A: Given function

Q: Consider the following. S-5x, F(x)={,2- 6X +9, x²-6x + 9, x > 6 Find the x-value at which f is not…

A: Consider the given piecewise function

Q: a) At how many points is f(z) discontinuous? b) At how many pints is f(z) not differentiable?

A: This is a calculus problem and I solved it in the next step.

Q: For what value of b is X - b b + l' x 0 continuous at every x?

A: The given function is gx=x-bb+1if x&lt;0x2+b if x&gt;0. If the above function is continuous at x=0,…

Q: Is the following bounded or unbounded and why? f(x,y) = ln(x2 + y2)

A:

Q: Consider the following. S-3x, f(x)={2 - 4x + 3, x > 6 Find the x-value at which f is not continuous.…

A: Given: f(x)=-3x              x≤6x2-4x+3,   x&gt;6

Q: Use Theorem 9.2.1 to show that T is not continuous at 0, no matter what value is chosen for b.

A:

Q: Suppose f is continuous on the closed interval [- 1, 3]. If Fis an antiderivative of f , which of…

A:

Q: If f is continuous everywhere except at x = 2, then f(x +1) dx is not integrable. True False

A: To check whether the given statement is True or False."If f is continuous everywhere except at x=2,…

Q: Which of the following is always true for integrable functions f and g? OSrw-dw]dx= [otwiax- frimax…

A: For integrable functions f and g

Q: Find a value of x, if any, at which/(x)= Vx- 27 is not continuous.

A: We will check the continuity of the function

Q: Evaluate f x2 dx using the limit defintion of the definite integral.

A:

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) &gt;0. Does f have a local…

A:

Q: Write the following limit as a definite integral on the interval [4, 9] where c; is any point in the…

A: SOLUTION-

Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: Use the prové thát 1 x| < ]x| fór áll * # 0. onclü X| S x| för åll x € R. Hint. Apply MVT to f(x) =…

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Q: For what value of b is Sx, g(x) bx?, x 2 -2 X<-2 continuous at every x?

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

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

A: From the given problem: 57).   fx=12x+1,x≤23-x,x&gt;2   As we know that, if L.H.L is not equal to…

Q: Consider the following. S-3x, f(x)={2 - 2x+ 9, x > 2 Find the x-value at which f is not continuous.…

A: We will find the value of x at which the f is not continuous and whether the discontinuity is…

Q: Consider the following function: f(x, y) = {xy cosy/3x2 + y2     if (x, y) 6 not equally to (0, 0)…

A:

Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

A:

Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

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Q: iii If the discontinuity of ƒ is removable, redefine ƒ so that it's continuous at 0

A: This question related to the topic continuity of real analysis.

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

A:

Q: At which point c does g have a removable discontinuity? How shouldg(c) be redefined to make g…

A: Removable discontinuity- if right limit gc+0 is equal to left limit gc-0 is not equal to gc, thengx…

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist. O…

A: For the solution of the problem follow the next step.

Q: If X is continuous on the interval 0 to 10, t O True False

A: For a continuous distribution, and there exist infinite points.

Q: If ƒ is continuous and f(t) dt = 16, find the integral

A:

Q: Given a2 +1, x 1. Is f differentiable at x = 1? Is it continuous at x = 1?.

A:

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: If f"(c) = 0, then f(x) cannot have a local extremum at x = c. %3D True False

A:

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

A:

Q: Consider the following. -8x, fx)=2- 8x + 5, X > 6 Find the x-value at which fis not continuous. Is…

A: Given function is f(x)=-3x               x≤6x2-8x+5      x&gt;6 The function is continuous at point…

Q: Let g be a continuous function. Using the substitution u = 3x – 1, the integral (g (3x – 1)) dx is…

A: We can use the concept of method of substitution in order to solve the given problem.

Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: 3. Suppose at t minutes, r(t) meters is the radius of a circular oil spill from a ruptured tanker…

A:

Q: If f(z) is continuous at z then it must be differenttiable at z, 0.

A:

Q: ) For a, 3 ER and B > 0, let f(x) ={} x° sin(|x|-#), when x # 0 when x = 0 0, ange of a and B (and…

A: Continuity and differentiability

Q: j(x) = v2x – 4 %3D

A: We have  jx=2x-4   Function is continuous when 2x-4≥02x≥4x≥2

Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

A:

Q: Find a constant b such that h is continuous at x = 2, where x +1 for |x| 2 With this choice of b,…

A: It is given that the continuous function  hx=x+1for x&lt;2b-x2for x≥2 It is also given that function…

Q: What is the continuous extension of f(x) = at point x-1. x -1 x2-1' %3D x +x-2 find dy dx

A:

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

A:

Q: d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT =…

A:

Q: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2

Q: d) Will h(t) be continuous or discontimuous at t = 3 if we use A = 1? If discontinuous, what type of…

A: Here we use the definition of continuity of a function at a point. Which is defined by Left hand…

Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2

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.