Let f be the function 6x-1 for x < -1 f(x) = { ax + b for - 1< x s 5x-1 for x > Find the values of a and b that make the function continuous. (Use symbolic notation and fractions where needed.)

Q: Find the values of x for which the function is continuous. f(x)=x3-6x2+x-3 all real numbers x > 0…

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Q: For the function f(x)=2x-3sqrt(x), explain whether the Mean Value Theorem can be applied to f(x) on…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: The given function is

Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

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Q: Which value of c satisfies the conclusion of the MVT for the function f(x) = -6x²-3x - 2 on the…

A: Solution-

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: Given: Since every differentiable function must be continuous.

Q: Let f be the function 3x-1 for x f(x) = 4x-1 Find the values of a and b that make the function…

A: Given: fx=3x-1for x&lt;-1ax+bfor -1≤x≤124x-1for x&gt;12

Q: Find the intervals where f(x) = x2e−x is increasing and where it is decreasing.

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Q: Find the constant a such that the function is continuous on the entire real line. [ 5x², x 2 1 x < 1…

A: The given function is: f(x)=5x2   ,   x≥1ax-3,  x&lt;1 To find constant 'a' such that the function…

Q: Find the intervals of monotonicity of the function f(x)=√x−x2.

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Q: Find the open intervals where f is increasing or decreasing. f(x)=ln|x^2-1|

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Q: For f(x)=3|x| does the Mean Value Theorem apply on the interval [-2, 2] and why?

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Q: For the function x2 +3 for x 2 | Identify the discontinuities of f as removable, jump, or in…

A: Given information: The function is hx=x2+3    for  x&lt;110-x   for  1≤x≤26x-x2  for   x&gt;2.…

Q: Find the domain of f(x) = 3x/(x − 1) and discuss the behavior of f near any excluded x-values.

A: Given function is f(x)=3xx-1 Since domain is the set of all those input values for which the…

Q: Find the value a that will make f(x)={2x^2-7x+3/x-3  if x is not equal to 3…

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Q: Find the absolute extrema of the function on the closed interval. 5x f(x) [-5, 5] x2 + 16

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Q: Let f(x) = x^2 −x −2. Using the Intermediate Value Theorem, explain why this function has (at least)…

A: The function is  f(x)=x2-x-2

Q: 2 For the real-valued functions f (x)=x´- 3 and g (x)= /x-4, find the compositionƒ °g and specify…

A: Given f(x)=x2-3 g(x)=x-4

Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

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Q: ,if x>2 Find the correct value of bb that makes

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Q: How do you solve question 4?

A: We are given the function, f(x) = x4 – 2x2 + 3x. Here, we need to show that the function f(x) has a…

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Find the intervals on which the function f(x) =x2 +5x2 -8x+1 is strictly increasing function

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Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

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Q: find the largest domain for f(x) = (x-3)2   with an upper x bound of 8 such that the function f is…

A: fx=x-32 Differentiating with respect to x, we get f'x=2x-3 Now function is non decreasing in the…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given information: fx=-x33+x22+2x

Q: If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

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Q: Find the constant a such that the function is continuous on the entire real line. 1 = √7x², lax - 5,…

A: Topic = Function

Q: find the intervals on which f(x) is decreasing f(x) = 2x³ – 3x² – 36x

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Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

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Q: Let f(x) = V 25 -– x2, 0< x < 5. (a) Find f-1. f-1(x) = (for 0 <x < 5)

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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…

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Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: Find the constant a, or the constants a and b, such that the function is continuous on the entire…

A: fx=3x2,      x≥1ax-4,  x&lt;1 Since fx is a polynomial function for all x&lt;1 &amp; x&gt;1,…

Q: Question in Image.

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Q: (b) Determine the values of a and b that make f(x) continuous for all real x. x² – 4 x- 2 f(x) =…

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Q: b) Find the Constants "a" and "b" such that the following function is continuous for all real…

A: We have to properties of continuity first.

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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Q: Find the intervals on which .5 * .f(x)=x/(x^2+4) is increasing )2 نقطة( f (x) %D x²+4 (-∞, -2) (-∞,…

A: In this question, we will differentiate the given function with respect to x . Then we put it equal…

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

Q: find the absolute extrema of f(x)= 4x^2-48ln(x) on the interval [.4, 5]

A: Given function is  f(x)=4x2-48ln(x) Differentiate both sides with respect to x. f'(x)=8x-48x Now,…

Q: Find the open intervals on which f(x) = x3 − 3/2x2 is increasing or decreasing

A: Find the open intervals on which f(x) = x3 − 3/2x2 is increasing or decreasing

Q: 3. For f(x) = x' + 14, find all x such that f(x) = -13.

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Q: Find the intervals on which the function f(x) =x3+5x2-8x+1 is strictly increasing function

A: ⇒f(x)=x3+5x2-8x+1⇒f'(x)=ddx(x3)+5ddx(x2)-8ddx(x)+ddx(1)⇒f'(x)=3x2+10x-8⇒f'(x)=3x2+12x-2x-8⇒f'(x)=3x(…

Q: Find the constant a such that the function is continuous on the entire real line. 5x², ах — 7, f(x)…

A: For a function to be continuous, the value of the left and right limits at critical point needs to…

Q: Find the constant a such that the function is continuous on the entire real number line. Sx³, x 2…

A: Given : f(x) = x3,x≤2ax2,x&gt;2 and the function is continuous. To find : value of a?

Q: Suppose that f(x)=x2 ln(9-5x2) find f'(x) and use interval notation to give the domain of f.

A: Solve the following problem

Q: (-x3 – 4x + 20 ,x > 3 2 – 7x , x < 3 Determine whether the function f(x) = is continuous at x = 3.…

A: From the given problem: fx=-x3-4x+20 , x&gt;32-7x , x≤3 As we know that:  If limx→a+fx=limx→a-fx=fa…

Q: f(x) = x² – 3x – 10 %3D

A: The limit of a function at a point is the value of the function when the value of the variable is…

Q: Let f(x)= 6-x and g(x)= ln(x). What is the domain of g o f(x)? Express your answer in interval…

A: This question is based on functions and definition of Natural logarithm.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.