х+ 2 if x <0 43. f(x) — { е" if 0 < x< 1 2 — х if x > 1 et -

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

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

A:

Q: What is the largest interval containing zero on which f(x) = sinx is one-to-one?

A: Such largest interval containing zero on which sin x in one to one is given below,

Q: Fermat's theorem states that if f has a relative extremum and if f'(x) exists, then f'(c) = 0.…

A:

Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a.…

A:

Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: On which interval is the function f(x) = tan x² continuous Is the function f(x) = ! - continuous at…

A: 3.1)  tan x2 =sin x2cos x2We know that sin x2 and cos x2  are both continuous functions.Thus, tan…

Q: 10 The function f(x) = - has a removable discontinuity at x = 2. To remove the - 2 discontinuity,…

A: Given: f(x)=10x+x2−4x−2

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: fx=sinx-1, 0&lt;x&lt;2π To Find: Increasing and decreasing function.

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to…

A:

Q: Is it possible to determine f (7) if f (x) = 3 for all x &lt; 7 and f is right-continuous at x = 7?…

A:

Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: What conditions must be satisfied by a function if it is to be continuous at an interior point of…

A:

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: Determine the location and value of the absolute extreme values of f on the given interval, if they…

A:

Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = sin x − 1, 0…

A:

Q: Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real…

A: Consider the given conditions for f(x) and assume the graph for function f(x) for the given…

Q: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

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: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: 64. Is the function given by f(x) = continuous %3D =2- 6x + 8 at x = 3? Why or why not?

A: We have to check the given function fx=1x2-6x+8 is continuous at x=3 or not. To check the continuity…

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: On the graph of f (x) = cos x and the domain -2n <x < 0, for which of the following interu is f(x)…

A: The Solution along with the graph is given below- Strictly Decreasing function - when x1&lt;x2 but…

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

A:

Q: For what value of k will the function f be continuous on (-0,0)? x² –100 f (x) = { * if x + -10 =…

A: Continuous function should not have any abrupt (sudden) changes.

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to…

A: Given : fx = x2-x-2x-2

Q: What is f (3) When x²-9 X-3 f(x) = x when XX3? Assume that f(x) is a function that is continuous for…

A:

Q: 2. Find the numbers at which fis discontinuous. At which of these numbers is f continuous from the…

A: The given function is f(x)=x3+1  if x≤13-x   if 1&lt;x≤4x     if  x&gt;4 We will check the…

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 2…

A: Given, f(x) = 2cox - x              x ∈ [ 0 , 2π] f'(x) = 2 (-sinx) - 1 = -2sinx -1…

Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

A:

Q: Consider the function f with domain (-2, ∞): 3|22 – 1| if – 2 < x < 1 2x2 + 2х — 4 f(x) = 3 if x = 1…

A: Solution is given below:

Q: Is it possible to determine f(7) if f(x) = 3 for all x &lt; 7 and f is rightcontinuous at x = 7?…

A: Solution: Consider the given that f(x) = 3 for all x &lt; 7 f is right continuous at x = 7  The…

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: Find the intervals on which f is increasing and decreasing. f(x) = - cos 2x on [-1,1]

A:

Q: Find the numbers at which the function is given   is discontinuous. At which of these points is f…

A:

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

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Q: Find the numbers at which f is discontinuous. At which of these numbers is f continuous form right,…

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Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: Prove that f(x) = x-¹/2 is: (i) not sectionally continuous in every finite interval in the range x ≥…

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Q: On what intervals is the function f(x) = x-4r both decreasing and concave up? Write your answer in…

A: fx=x4-4x3 Differentiating with respect to x, we get f/x=4x3-43x2    ∵dxndx=n·xn-1=4x3-12x2 Again…

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: Given, fx = x2-2x-3x-3  We have to define f3 in order to make f is continuous at 3.

Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

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Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

A:

Q: Where is the function f(x) below discontinuous? if z 2 Choose all answers that apply. f(x) is…

A: This question is related to limit and continuity, we will solve it using given information.

Q: x' - 8 24. f(x) : x? – 4

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.