PROBLEM 4: Consider the functions k(x) = V3x + 1, h(x) = 2 – 7x a) Find (k o h)(x). (k o h)(x): b) Find the domain of (k o h)(x). Express answer using interval notation. Domain of (k o h)(x):

Q: 1. Determine the particular solutions of the following function. (D3 – 3D – 2)y = 0; when x = 0, y =…

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Q: Problem 1: Given the piecewise function f(x) x -1 x 2 2 a. Determine the values of m and n so that…

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Q: Part d please

A: Left hand limit of x=0 is=0+1=1Right hand limit of x=0 is= -infinity So, at x=0 it is discontinuous

Q: QUESTION 6 Suppose f'(x) =x4+x3– 6x2. Determine the value of x where f has a relative maximum value.…

A: The solution of the problem is given in the next step.

Q: 26. Consider the functions y = f(x) and y = g(x) whose graphs in red and blue, respectively, are…

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Q: Problem 1: At what points is the function y = form. 2x²+10x+12 x²-5x continuous? Write your answer…

A: In this question, we want to know the points (in the form of interval) at which the given function…

Q: QUESTION 6 A critical point of the function occurs at an interior point c: when eitherf'(c) = 0 or f…

A: Critical Point:- A critical point is a point in the domain of the function where the function is…

Q: 3. Consider the function f(x) = 23 if x = Q if x # Q. Prove that f'(0) = 0. Hint: Apply the…

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Q: PROBLEM: B. Find the absolute maximum and absolute minimum of the function f(z) -z-8z +7 over [1,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: QUESTION 1 Determine the symmetry of the function. f(x): to x² + 2 O Even О odd O Neither О Both

A: If f(-x)=f(x), even If f(-x)=-f(x), odd

Q: Question 1) Find the absolute maximum and minimum of the function f f (x, y) = yx² where - 2<x< 2 -…

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Q: Question 2: Identify the co-ordinates of any local and absolute extreme points and inflection points…

A: Given function is  Y=4x3+21x2+36x-20find local and absolute extreme points and inflection points for…

Q: Problem 1. (a) Prove that the function f(x) = x³ – 4x + 2 has three distinct roots in the interval…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Question 2 Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f…

A: Topic  = Derivative    Rolle’s theorem states that if a function f is continous on the closed…

Q: Problem: 3 a. Find the domain of (fo g)(x) if f(x) = and g(x) 3x-1 %3D x+4 %3D 5x-2 ズー1

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question…

Q: Question 9 Ay f (x) =< ; Estimate f (-2) %3D 8-6 4 O -1 -2 O None of these 2]

A: The graph of the function crosses the x-axis when x=-2. Then, the value of the function at x=-2 is…

Q: PROBLEM 4: Graph the function y = 2x5 - 2x* + 3x3 – x +1 for interval -2 <x < 2 by showing the…

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Q: Question 2 Given the function k with k'(x) - and b a real number such that b > 0. If the domain of…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: QUESTION 4 Find the domain of the function. f(x) O [9, = -4x + 9 *) (0, ) O (*, *) O (*, 0) U (0, *)

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Q: Question: 4 Find the value of "k" such that the function f(x)=x² + kx-6 satisfies the hypothesis of…

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Q: Sketch or graph f(x) X, -T <x < 0 = LT - x, 0 < x < Tt Problem 1: f(x) |

A: Given  here we can see from -pi to 0 graph would be a straight y = x axis  and from 0 to pi graph…

Q: 1. Fit the function g(x) = v1x + v2 (x – 1)3 to the data in table below. Xi -1 1 Yi 2 1 -1

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Q: Work Problem 2( Question 1 ( Use the First Derivative Test to find the local maximum and minimum…

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Q: PROBLEM: B2 Find the absolute maximum and absolute minimum of the function f(z) = 1-4z +3 [1, 4].…

A: The given function is: f(x)=x2-4x+3 To find its absolute maximum and minimum over [1,4].

Q: QUESTION 13 Find the domain of the function. 2x g(x) %3D x2 - 4 (-00, 0) O (4, ») O (-x, 0) U (0, o)…

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Q: 3. Consider the function f(x) = -{2 if x = Q -r³ if x # Q. Prove that f'(0) = 0. Hint: Apply the…

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Q: Question #5 Let [x², x 1 f(x) = Draw the graph of f(x) and discuss its differentiability at x = 1.

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Q: The function graphed to the right is of the form y= c+ cos x, y= c+ sin x, y= cos (x-d) or y = sin…

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Q: 2 – 16 Problem 8 Consider the function f (x) = x² – 3x – 4° (а) State the domain D for f (x) using…

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Q: Find the global maximum and minimum of the function on the given interval:f(x)=x2−2x+5,x∈[−1,4].

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Q: Problem 2: Given a function 4x-1 f(x) = 2x +1 Use tabular method to determine if the limit of a…

A: we make chart of the values of x and the value of f(x) to see trend toward the limit…

Q: Problem 7. Suppose that the compler-differentiable function f: C has a primitive F on 2. Does it…

A: Suppose that the complex differentiable function f:R→ℂ has a primitive F on R then it may not follow…

Q: Sketch a graph of the function f(æ) = – sin(x). -T/4 T/4 /2 3n/4 5t/4 3n/2 元 7/4 -1

A: Given: A function, fx=-sinx. -sinπ4 -32 -sin0 0 -sinπ2 -1 -sinπ 0 -sin3π2 1 -sin2π 0…

Q: Problem 2: Determine whether the function f (x) = 3 - Vx+9 is continuous on the interval [0, 1.

A: Given that:   *The function f(x) is, Since the given function is in fractional form and the…

Q: Question: 2 Find the absolute maximum and minimum values of function f(x) = 3x - 2 - 2x over the…

A:

Q: QUESTION 5 2 The absolute minimum of f(x)= 3 x3-2x 0n [-1,8] is y= OA OB5 OC OD.

A:

Q: Problem 1. Suppose f: R → R is a continuous function which can be uniformly approximated by…

A: Given: A function f: R → R is a continuous function that can be uniformly approximated by…

Q: Question 8 Let f(x) = | x-, x <1 2x+3, x21 Compute f'(1)

A: Recall: The derivative of a function at 'c' exists if  (i) Right hand derivative at 'c' exists .…

Q: Problem 10. Find the interval where f is increasing or decreasing, and find the loca maximum and…

A: Given problem:- Find the interval where f is increasing or decreasing, and find the local maximum…

Q: Problem 7: Sketch the domain for the function f(x, y) = In((x – 1)0+1))

A: Given function: f(x,y)=lnx-1y+1

Q: Problem 3. Let f(x) = (r2 - 6x + 4)e-/2. Determine the interval where f(x) is strictly decreasing.…

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Q: Question: 9 a)Use the second derivative test to determine whether the function has a local maximum…

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Q: Question 3. Find the absolute maximum and absolute minimum of the function f(x) = 3.x2/3 – x on the…

A: To find the absolute maxima and absolute minima of the following function  f(x) = 3x2/3 - x  in…

Q: Question 6. Consider the function f : R² R. f(r1, T2) = 8r1 – 4r7 +2r,I2+2r2- 3r3 +10. • If the last…

A: Step:-1 Given that fx1, x2 =8x1 -4x12 +2 x1x2 +2x2 -3x22 +10 subject to  x12 +4x22 ≤1  and  x1+x2≤1…

Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: QUESTION 11 Suppose f'(x) =x4+x3– 6x2. Determine the value of x where f has a relative maximum…

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Q: Find the global maximum and minimum of the function f(x)=√3−2x on the interval [−3,1).

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Q: Problem 3 Find the absolute extrema of the function f (x) =7sin(3x)– 3x In the closed interval [0,…

A: To determine the absolute extrema of the function.

Q: Question 4 Suppose f(x)=x+x3-6x2. Determine the value of x where fhas a relative maximum value. A…

A: x=-3 is the point of a relative maximum value

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.