87. Suppose that f and g are continuous functions such that, for all a, := | g(x)dx Give an intuitive argument showing that f (0) = g(0). Explain your idea with a graph.

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

A:

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

A:

Q: 2. Given the function f(x) = ., determine if the function is continuOus or not. Identify the point/s…

A: Given function f(x)= (x2-1)/(x-1) is continuous or not , determine type of discontinue.

Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x&gt;5 We have to find the value…

Q: If the limit of f(x) is 1 as x approaches 1 and the limit of g(x) is infinity as x approaches 1,…

A: we have to find the limit of the following

Q: (b). Show whether (*) is continuous at *=-2, if (3x-2 for x = -2 S(x)=. x? - 4 х- 2 for x * -2

A:

Q: Q4: Use the limit definition to compute the derivative, f(x), for 2.F(x) = Vx³ – x

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: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: 10 if x c - everywhere then: С —

A:

Q: if x < 6 cx2 + 7x x3 - cx Let f(x) = if x 2 6. For what value of the constant c is the function f…

A:

Q: Q4: Use the limit definition to compute the derivative, f(x), for 2 1.F(x) = xi

A:

Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: Suppose g is the function defined by picture where k and m are constants. If g is differentiable at…

A: Solution

Q: If Зх — 2,х <3 -{ - h(x) х4 — 74, х 2 3 Is h(x) continuous at (x=3)? 1 Add file

A:

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: If limit t y = f(x) write an expression for the differentia dy

A: Given: y=f(x)

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: Is the functionf graphed below is continuous at x= -1? Choose the appropriate reason that justifies…

A: Continuous at x=-1, as limit is equal to f(-1).

Q: Q4: Use the limit definition to compute the derivative, f(x), for 1.F(x) = x3 2.F(x) = = Vx3 - x

A:

Q: be the continuous function defined on [-6,6] whose graph consists of a quarter circle mree line…

A: the solution is clear from the graph

Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

A:

Q: 6. By considering different paths of approach, show that the following function has no limit as (x,…

A: given f(x,y)=5x2yx8+y2we need to show that the following function has no limit

Q: For what value of the constant c is the function f continuous on (-∞, 0)? if x 5 C = Need Help?…

A:

Q: Suppose f" is continuous on (-o, 0). (a) If f'(2) = 0 and f"(2) = -2, what can you say about f? (b)…

A: Application of derivative problem

Q: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

A:

Q: Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: x+4 if x2

A:

Q: Give the graph or the formula of a function that is continuous but not differentiable at x=0.

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Q: f(x)=√√x at x = 7

A:

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: Start with g(x) = 3x. Use the limit definition of the derivative to show what g'(x) is.

A:

Q: _18. Determine the following function if continuous at f(x) = ) `x + 1' ; at x = 0

A:

Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

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Q: Suppose that ƒ is a continuous and differentiable function s 2000 and that f'(x) > 7 for all x. What…

A: Lagrange's means value theorem: -Let f: [a, b] R be a continuous function on [a, b] and…

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

A: