function is defined as c*x^1 from 1 to 5 and 0 otherwise. What is c?

Q: Prove: f(x)=5x is continuous at x-2

A: Given function is fx=5x,

Q: Either a function is not differentiable at a point or it is continuous at that point. O True False

A:

Q: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: Е, (2,3)

A:

Q: 4 if x3 to define f at x = -2 in such a way that f becomes continuous nossible what ie the velue of…

A: We have to find the following conditions according to the given information

Q: Fill in each blank so that the resulting statement is true.

A: We know, A function f is continuous at a when three conditions are satisfied. f is defined at a,so…

Q: Sketch the graph of a function f  that is continuouson [1, 5] and has the given properties.   f has…

A: f is continuous on [1,5]. f has no local maximum or minimum. 2 and 4 are the critical numbers.

Q: Can we evaluate the limit using f(c) if the constant c will not make the function undefined or…

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

A: we have;  f(x)=x32

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

A: We  will compute the derivative of given function  by using first principle of derivative

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x<5x+1            ,  x≥5

Q: _25. Determine if f (x) = {"" (2x – 1 if x 5 is continuous on [2,5]. A. discontinuous on an…

A:

Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

A:

Q: Show that f (x) = is not uni form continuous on (0,3) -3

A: To prove that 1x-3 is not uniformly continuous on 0,3

Q: Find Lebesque integrae of function segment (-4,0) On f(x) = Txen X+4 O a. 12*41/3/5 O b. 3*41/3/5 O…

A: In R if a function is integral the lebesgue and Riemann gives same value

Q: Show that the functions are continuous on their natural domains with examples?

A:

Q: Sketch a graph of a function f that is continuous on (-0,0) and has the following properties. f'(x)…

A: Given that: f'x<0 and f''x<0 on -∞,3; f'x<0 and f''x>0 on 3,∞. We know that if, f'x>0…

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1<x2 then fx1>fx2 claim- is it decreasing or increasing

Q: Which of the following family of functions are not known to be globally continuous (ie, contin- uous…

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: If f is continuous on (-x, ∞), what can you say about its graph?

A: If f is continuous on (-oo oo) what can you say about its graph?

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

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Q: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x&lt;1           x…

Q: Draw the graph of a function f on [0, 4] with the given property. Infinite one-sided limits at x = 2…

A:

Q: Consider the following. f(x) = |x < 1 |x|21 Find the x-values at which fis not continuous. Which of…

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Q: Show that ( if f is decreasing is riemann)

A:

Q: If f(z) is analytic function show that:

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Q: and the domain of the function using interval notation. To enter ∞o, type infinity. To enter U, type…

A: We can solve this as follows:

Q: If function fis continuous on [-10,5], then which of the following statements must be true?

A: Remember : If a function is continuous on the [a,b] then it is differentiable on (a,b) and if it is…

Q: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

A:

Q: Suppose f " is continuous on (-∞, ). (a) If f '(-5) = 0 and f "(-5) = 5, what can you say about f ?…

A: Given:

Q: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: Suppose that a function f(x) is discontinuous (i.e., not continuous) at x=c. Then it follows that. O…

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Q: If n= any integer, show that the function f(z) +[- z] has %3D removable discontinuity at x-n, here…

A:

Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: Suppose that the functions f and g are defined throughout an open interval containing the point x,,…

A:

Q: Show that f (x) =++1 1 - is not uni form continuous on (-1,0)

A:

Q: 5. Find three relation from {1, 2} to {6, 7} that are NOT functions.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the value (i.e. what do we learn) from using the Wronskian on a set of functions?

A: Let F = { f1, f2, f3, ...fn} be the set of functions. 1. If W(f1, f2, f3,...fn) =0 Then we say…

Q: Find f"(x) if f (x)=√√5 - 4x. Show work:

A:

Q: Verify the Mean Value Theorem for f(x) = In(6x + 1) on | 0, %3D

A:

Q: estimate the type of the function at the interval {(1,2), (2,5), (3,5), (4,7)} is it: 1-1 or onto..?

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Q: let ļ be continuous decreasing is an even function, Heen e increasing [-b, -a] on

A:

Q: Sketch the graph of a function continuous on the given interval that satisfies the following…

A: Given, f is continuous on -∞,∞; f'(x)&lt;0 and f''(x)&lt;0 on -∞,0; f'(x)&gt;0 and f''(x)&gt;0 on…

Q: Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on (a, b),…

A: Given, Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on…

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: draw the graph of a function f on [0, 4] with the given property. Infinite one-sided limits at x = 2…

A:

Q: 6. For each of the cases, give an example of function f: Z → Z. Verify your examples. (a).…

A:

Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

A:

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.