1. Find the value/s of b such that the function f is continuous everywhere. x3 + 2, x < 0 f(x) = {5x – sin bx x > 0

Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: Find the value of c that makes the function continuous at x = 0. SNIPP

A: Hence it is given that the given function is continuous, so we can write:…

Q: So, 0, -T < x < 0 f (x) = sin x, 0 < x < T

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Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: 1. Find if the function is continuous in the given points (sin(x+y) x+y 1 D) f(x, y) = x + y = 0…

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Q: Q:A Function is defined as follows sin f(x)= x +0 x = 0 what condition should be imposed on m so…

A: For the given function to be continuous , the conditions required is

Q: (1.8) Consider the function: { sin 2x if x # 0 In a if x = 0 f (x) = Write down the value of a for…

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Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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Q: Find a value of c that will make the following function continuous at x = 0. sin² 4x x ≤ 0 x² f(x) =…

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Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, f" () -1, and g(x) = log…

A: Differentiate two times at given value

Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: Find the absolute maximum and absolute minimum of f(x) on the given interval f(2) = (-1,2) %3D x²…

A: 1) fx=x2x2+1, -1,2 Differentiate f(x) with respect to x…

Q: Find the maximum and minimum values of the function f(x) = x – sin x on [0, 27). %3D

A: The given function is: f(x)=x-sinx For maximum and minimum value, differentiate the function and…

Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: -x² +1 1- sin? x if x20 if x <0 Let f(x) be defined as f(x)= • Is f(x) differentiable at x = 0? • Is…

A: Answer and explanation is given below..

Q: (sin x - a ((x) = {cosx +b -nsx<0 e -1 x<-T x20

A: Topic = Continuity a=2 b=-1

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: 3. Find the constant "a" such that the function is continuous on the entire number line. 4 sinx x< 0…

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Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: Suppose that the function f(x) and its first derivative have the fol- lowing values at x = 0 and x =…

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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: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: The limit of f(x) = sin(x) as x approaches t is O T/x n/2

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Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: 1. Use the properties of continuous functions to explain why f(x) =x cos(x) +1 is a continuous…

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Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

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Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

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Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: How would I go on getting the max and min for this trig problem?

A: We first find the critical points in [0,2pi] by solving f'(x)=0

Q: Consider the function given by V2 + x x² – 4 x<-2 g(x) = -2 <x<0. x + 2 2 sin(7x) 0<x Determine if…

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Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: 1. The range of y=-e* +2 is (-0,1). 2. The function f(x)=sin x+cos x is an odd function. 3. lim

A: Topic:- function  Topic:- as per our guideline only first three subparts need to be answered.

Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

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Q: Find the local maximum and minimum values of the function g (x) =x + 2 sin x   ,  0&lt;= x &lt;= 2…

A: Given that : The function is g (x) = x + 2 sin x , 0 ≤x≤2π .

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: 7. Find all values of x on the graph of f(x)=(x-1)´(2x+1) at which the tangent line is horizontal.…

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Q: (1) Locate the absolute extrema of the function on the closed interval. (a) y=4 sin x, [0,2n] (b)…

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Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: 1. Find the value/s of b such that the function ƒ is continuous everywhere. f(x) = {6x – sin bx 0 <x

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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

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.