Show that the function is continuous over ]-infinity, +infinity[ 4 x* sin(1/x) si x#0 f(x)=: si x=0

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

A: Introduction :We have given a function f(x) we have asked to calculate the value of k , if f(x) is…

Q: Define g : R →R x sin (1/x), g(x) = 10, x # 0 x = 0. Explain why g is continuous at 0; in…

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Q: consider the function f defined on [0,∞),f(x)=(x^r)sin(1/x),for x≠0 and f(x)=0 and for x=0, where r…

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

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Q: Consider the functions f(x) = cos(x) and g(x) = x--1 over the interval

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Q: Let f : [0, 1] → [0, 1] and f be continuous on [0, 1]. Show that there exists x E [0, 1] such that…

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Q: Consider the function ), x + 0 x cos f(x) = x = 0 0, a. Show that f is continuous at x = 0. b.…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Let f be the function defined by: sin x, x <0 x2, 0 <x < 1 2 - x, 1<x < 2 x-3, x22 f(x) = %3D For…

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Q: Consider the function (). xチ x +0 cos f(x) 0, x = 0 a. Show that f is continuous at x = 0. b.…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Is the function continuous on the interval 0, 27? 1+(sin z)? O yes O no cannot be determined

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Q: Find all values of c such that f is continuous on (-∞, ∞). f(x) = { S 5- a², x >c (smaller value) C…

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Q: Find all values of c such that f is continuous on (-o, 0). { 7- r, /(r) – (smaller value) (larger…

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Q: Find all values of c such that f is continuous on (-0, 0). 1- x2, f(z) = { – x², x. C = (smaller…

A: Given function is, fx=1-x2   , x≤cx          ,x&gt;c  Since 1-x2 and x are continuous on the…

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Consider the given function: fx=xsinx Here, the objective is to determine the domain of the function…

Q: 1. Consider the function f defined on [0, 0), f (x) = {x* sin- x + 0 x = 0 where r > 0. Determine…

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Q: if the function f below is continuous at x = 1: f (x) = {1-√1-x, x ≤ 1 ln x, x ≥ 1}

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that J f(x)dx = A, f(x)dx = B, and…

A: Given: ∫05f(x)dx=A∫03f(x)dx=B∫53g(x)dx=C…

Q: 1. Define the function [In(x + 1)] cosh x + tan x ,x > 0 (sinh x) sec-(x - 2) f(x) = , X < 0 a. Show…

A: Here, the given function is: f(x)=[ln(x+1)] cosh x+tan x, x≥0(sinh x)sec-1(x-2).       x&lt;0

Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

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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: a) For which values of a and b in R is f(x) continuous on (-infinity, pi/2)? b) For which values of…

A: Given function is f(x)=x+a, x≤0bcos(x)+asin(x) , 0&lt;x≤π4btan(x), x≥π4 If f(x) is continuous on…

Q: Determine where f'(x) exists, an expression for it, and where f'(x) is continuous: f(x) =D |…

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that f (x)dx = A, f(x)dx = B, and…

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Q: a. Let f(x) be a function satisfying |f(x)| < x² for –1 < x < 1. Show that f is differentiable at x…

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which 5 f(x)dx = 4.…

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Q: True or false: if f(x) is continuous at x =a, then f(x) is differentiable at x =a.

A: We have to determine the given statement as true or false.

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: Determine the set of values of the continuous function defined by the formula: T COSX b) g(x)= sin 6

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Q: 2. Let f be a differentiable continuous function on [a, b] and suppose f' is continuous on [a, b].…

A: In this question we will use basic of calculus i.e properties of integration. We will use…

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: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

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

A: A function f: X -&gt; Y is said to be one-to-one, if the images of distinct elements of X under f…

Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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

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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: Determine the extrema of the function on the given interval, if there are any, and determine the…

A: gx=x2+cosx2 on -π, π. Differentiating with respect to x, we get g'x=2x+-sinx2·2x=2x-2x…

Q: ind the absolute maximum and minimum values of f on the given interval. a) f(x) = on [0, 2] g2+1 on…

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Q: Let f(x) = x arctan(1/x) if x 0 and f(0) = 0. (a) Is f continuous at 0? (b) Is f differentiable at…

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Q: 3. Let f(x) = sin(-x²). Find a formula for F such that F'(x) = f(x).

A: If  ddx(f(x))=g(x) Then; ∫g(x)dx=f(x)+C Where C is the constant of integration.

Q: 1. Consider the function f defined on [0, 0), Sa" sin- f (x) = x = 0 where r > 0. Determine the…

A: The solution are next step..

Q: 1. Consider the function f defined on [0, ∞), 1 f(x) = {x' sin-, x# 0 x = 0 where r > 0. Determine…

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Q: f(x) = (sin x – 1) cos x on 2'2.

A: I am attaching image so that you understand each and every step.

Q: Consider the functions f(x)= x3-1 and g(x)=−2x+sin(x). Show that there is exactly one C in (−∞,∞)…

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that | f(x)dr = A, | f(x)dx = B,…

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Q: 3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x)…

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Q: 3. Let f(r) = r sin() if z #0, and f(0) = 0. Show that f is continuous at r= 0 by using e- d…

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Q: a) f is continuous on [0,∞] b) f is differentiable on [0,∞) c) f' exists and is differentiable on…

A: Given: The function is  f(x) =xr sin1x ,         x≠00,                     x=0

Q: (c) Use only the e – 8 definition of continuous functions to directly prove f(x) = x² sin(x) is…

A: In the given question we have to solve the part c of the given question. In this part we have to…

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.