Let f be the function defined by: sin x, x <0 x2, 0

Q: Q1. In process to prove that f(x)=sin(x -x]) is continuous, we apply the composition of two…

A: We know that the composition of function is defined as (g o h)(x) = g(h(x))

Q: Find f(x) if f°(x)=cos x with f(0) =1, f'(0) = 2 , and f'(-)=3.

A: Keep on integrating we are end up with an answer. For those constants we need these initial…

Q: Let f(x) be given by the function f(x) = { 9(x)+a, 13 – b cos x, where a and b are constants x > 0'…

A: To show that f(x) is continuous at x=0

Q: Let f be a continuous function such that f(x) dx: = -1 and f(x) dx = = 9. %3D 2 2 | f(x) dæ? What is…

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Q: Let f(x)  = tan x . Show that  f(0)  = f(π)   but there is nonumber c  in  (0, π)such that f'(c )…

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Q: Determine if the function f below is continuous at x = 1: [1– VI– x, x 1

A: We have to find

Q: (tan ) 1/x TC + x 4 * f(x)D. k, For what value of k, f (x) is x =0 continuous at x = 0?

A: The

Q: Let f be a function which is continuous on the interval [a, b]. The definite integral of f on [a, b]…

A: n is nothing but (b-a)/∆X mean,    n=(b-a)/∆X

Q: The function f is a composite of two continuous functions: y = cos x and y = x 2, so f is continuous…

A: The function fx is a composition of functions y=cosx and y=x2and it is a continuous function.

Q: Determine f(5) if f is a continuous function that satisfies +sin(a) f+sin(a) f(t)dt = 22² for all x.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let f be defined piecewise as follows: kæ sin(x – 3) + 4, if ¤ < 3 f(x) = I – 3 4x2 + k, if æ 2 3…

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Q: Let y=f(x)be a function, defined implicitly by 2(x-y)=3 +cos y, that is continuous on the closed…

A:

Q: Explain why or why not f(x) is continuous or not continuous at x = 1 using the ideas of the delta…

A:

Q: Consider the following piecewise defined function: sin(ax) -1 < x < 0 4x f(x) = a2 –(b+1)x+b x²+x-2…

A: Given function is f(x)=sin(ax)4x,-1≤x&lt;0x2-(b+1)x+bx2+x-2,0≤x&lt;1x2-1+a ,1≤x≤2…

Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

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Q: Show that the function is continuous. f(x) = cos(x 2)

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Q: Let f(x) = x?sin (-) for x + 0 and f(0) = 0. c) Show that f'is not continuous at x = 0.

A: Given function  f(x)=x2 sin1x      for x≠00                  for x=0 we have to show that f' is not…

Q: be* + a + 1, x 1

A: The given function is  fx=bex+a+1,  x≤0ax2+bx+3, 0&lt;x≤1acosπx+7bx,  x&gt;1 To find the values of a…

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: Let f be the function defined by: sin x, x 2 - For what values of x is f NOT continuous?

A: Given function is: fx=sinxx&lt;0x20≤x&lt;12−x1≤x&lt;2x−3x≥2

Q: Let f be defined piecewise as follows: kæ sin(x – 6) + 4, if x 6 For what value of k is f…

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Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

Q: Is the function f (x) below continuous on [3,+0)? (0, x > 0 X, 0 3 Choose

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

Q: Find ao of the function f(x) 1-Cosx f(x) =

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Q: Let f be the function defined by f (x) = x cos x – sin x. What is the absolute maximum value of f on…

A: The given function is: f(x)=x cos(x)-sin(x) ;                   x∈-π2, 2π

Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: Find a value of k making h(x) continuous on [0, 5]. kx , 0 < x < 1 h(x) = x +3, 1<x < 5

A: Given: hx=kx,0≤x&lt;1x+3,1≤x≤5 given function will be continuous over 0,5, if it will be continuous…

Q: Describe the interval(s) on which the function is continuous. f(x) = cos 1/x

A: Given- fx=cos1x To find- The intervals on which the function is continuous. Concept Used- As we know…

Q: Let f(x) ∈ R[x]. Suppose that f(a) =0 but f'(a) ≠ 0, where f'(x) isthe derivative of f(x). Show that…

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Q: Which of the following functions is continuous on the interval (-0, +)? …* f(x) = Vx² – 1 (A f(x) =…

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Q: Find a value of x, if any, at which f(x) = Vx – 8 is not continuous. If f(x) is continuous for all…

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Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

Q: Determine if f is continuous at the indicated values. x = 0 f(x) = 1 sin x x + 0 a) x = 0. ? b) x =…

A: Given

Q: Consider the function x sin x> 0 f(x) 0, a. Show that f is continuous at x = 0. b. Determine f' for…

A: The given function can be written as (a) To check the continuity at x=0 Since, Therefore, f(x) is…

Q: Find the constant a such that this function g(x) is continuous on the entire number line.

A: Given,

Q: Let f be defined piecewise as follows: kæ sin(x – 3) f(x) + 6, if x 3 For what value of k is ƒ…

A: Given,         f be defined piecewise as follows :         fx=kxsinx-3x-3+6 , if x&lt;36x2+k , if…

Q: Let f be a continuous function such that 10 9 f(x) dx = 5. What is the value of f(x) dx = -6 and…

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Q: 87. If f is continuous and f(x) dx 10, find f(2.x) dx. %3D

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Q: Consider the function f(x) over the interval 0, 1. Does the extreme value theorem guarantee the…

A: Given function is f(x)=1sin πx4 over the interval 0, 1 and  q(x)=4x+32x2-1 Extreme value theorem: If…

Q: Let f be defined piecewise as follows: kæ sin(x – 3) f(z) = + 4, if æ 3 For what value of k is ƒ…

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Q: Show that the function f:R to R defined by f(x)=5x-12 is continuous using the E-d definition

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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: Let f(x) be continuous on [0, oo) and twice differentiable on (0, co). If f'(x) > 0 and f"(x) 1,…

A: Let f(x) be a continuous function on [0,∞) and differentiable at 0,∞. The given double derivative…

Q: Determine the set of values of the continuous function defined by the formula: a) f(x)=cos sin

A: Given that fx=cosπ3sinxgx=π3sinxsinx is continuous in x∈-∞,∞gx is also continuous in  x∈-∞,∞.Range…

Q: Consider the function f(x) = over the interval [0, 1]. Does the extreme value theorem guarantee the…

A: Given function is, f(x)=1sinπx4 over the interval [0,1]   In general there is no guarantee that a…

Q: sin(bx) x0. Find a value of b such that f is continuous, or explain why no such value exists.

A: Given, f(x)=sin(bx)xx&lt;0exp(x+5)x≥0