Based on the definition of Fundamental Theorem of Calculus, what instances in your definite life that you can narrate to the relationship between F'(x) = f(x) (e.g. effort and success, golden rule, or your principles in life)?

Q: Without a calculator, identify the given key features of the polynomial and sketch a possible graph.…

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Q: 2.) Evaluate the function for the given value of the independent variable. Simplify your answer if…

A: Note: As per our guidelines, we can solve first question. But I solved first two as your first two…

Q: 2. Find ƒ' (a) using f(x) = 3x² - 4x + 2. three-step rule if

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Q: Find the derivative of the function. X y = XV 16 – x2 + arcsin 5 y' =

A: given function find the derivative

Q: Estimate the intervals on which the derivative is positive and the intervals on which the derivative…

A: The derivative is positive (where the graph is going upwards) on the intervals and  the derivative…

Q: Find the solution of the differential equation y(t) = 1 y sec [x² + + 500 ( 7 ) x = 5000 (7) 44…

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Q: You are given the differential equation satisfying y/(2) = 6. The solution can be written in the…

A: given

Q: Let f(z) = (-6z— 4) (9z — 1)

A: f(z)=(−6z−4)(9z−1)

Q: Choose the correct graph for A and B

A: We have to choose the correct graph.From the conditions of Reimann sum we know that-If f is…

Q: Part II. Separation of Variables dy Solve the differential equation: = y(y + 2) dx Ans: In 2 = 2x…

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Q: The following figure shows the graph of f and a line tangent to the graph of f at x = 6 . Find f(6)…

A: The following figure shows the graph of f and a line tangent to the graph of f at x = 6.We find f(6)…

Q: Let f(x) = -2x√√x + f'(x) = -8 x²√x

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Q: Determine the quadratic function of the form f(x)= a(x-h)² + k whose graph is given on the right.…

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Q: f(x) = x x + 1 P(-2, 2)

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Q: 2) Given the function below, determine the intervals on which the function appears to be increasing,…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: The area under the curve y = √x bounded below by the x-axis and on the right by x = 4 is 16/3 square…

A: Solution:Area=Let t=-x==Area==Area=Similarly,Area=Let t=xdt=dx==Area=

Q: Suppose that V(t) = (28)1.07⁰ + 5 sin(t) represents the value of a person's investment portfolio in…

A: To find the instantaneous rate at which the portfolio's value is changing on January 1, 2022,  we…

Q: im ²/1 In (4+¹) is Af'(4) where f(x) = ln x (B) (4) where f(x) = (In x)/x (C) f'(0) where f(x) = ln…

A: To find:-

Q: Decide from the graph whether a limit exists. If a limit exists, find its value. lim F(X) X→-4 www…

A: Here we will find the limit from the graph using the concept of left hand and right hand limit

Q: Find the area of the shaded region. + -6 -5 -4 -3 -2 square units 8+ y y = x³ · y = x + 6 4 X

A: Consider the graph

Q: Find each of the following for the piecewise function: f(x) = f(-4)= 3 x² + 3 -2x + 4 x 2 f(-5) =

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Q: In three to five sentences, discuss how the Limits of a Function is relevant to optimizing the area.

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

Q: Separate the variables: Find the solutions of the following ordinary differential equations…

A: As per the guidelines,  I can only answer one question and rest of the questions will be reposted.

Q: In how many different ways can 5 identical green shirts and 5 identical red shirts be distributed…

A: 5 identical green shirts and 5 identical red shirts be distributed among 6 children such that each…

Q: 1) Given the functionf(x) = ln(x² - 169). a) Find the domain off. b) Find all the values such that…

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Q: 39. A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream…

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Q: What position vector is equal to the vector from (1, − 3,4) to ( − 2, – 6,1)? The position vector is…

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Q: Find proju if scalu = − 3 and v = ( − 1,4, - 8). proj, u = ( (Type integers or simplified…

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Q: 3) Given the functionf (x): = 2(x²-25) x²-4 a) Identify the horizontal and vertical asymptotes and…

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Q: 9. Evaluate the integral by changing to spherical coordinates. вто St √2-x²-y² √√x²+y² xydzdydx

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: 4. Determine the distance between the point (1, 0, 1) and the plane [x, y, z] = [1, 2, 3] + s[2, 1,…

A: GivenEquation of plane

Q: The graphs of the functions f and g are shown below. If h(x) = f(x) · g(x), find h' (5). Y

A: given graph of f(x) and g(x)and h(x)=f(x)g(x)

Q: 20. (1.4.2) Use the Law of Exponents to rewrite and simplify the expression. a) 83 b) x(3x²)³)

A: a) 84/3b) x(3x23

Q: The area under the curve y = √x bounded below by the x-axis and on the right by x = 4 is 16/3 square…

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

Q: - 43-46. Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: =-8x-1 = x³-2x+7

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Q: 9. The position of Minnie the mouse, as she moves back and forth along a horizontal line is given by…

A: Given that  position of Minnie the mouse given by equation is

Q: We are told that sand is creating a cone-shaped pile that is growing in size as sand is added. We…

A: GivenRadius = rheight hThe diameter of the base of the cone is approximately three times the…

Q: 8. (1.1.74) If f and g are both even functions, is the product fg even? If f and g are both odd…

A: if f(-x)=f(x) then f is called even function.If f(-x)=-f(x) then f is called odd function.

Q: Consider the following two lines in space 1 2 = 6t , y =ut y = 4 +5₁ 2 = −1+S 72=X :17 2₂: X=15

A: Given that the following two lines in space

Q: Prove the formula, where m and n are positive integers. sin(x) sin(x) dx = [0 men (xif m=n Let m and…

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Q: Find the indicated derivative. dx dy dx = for y = x14

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Q: 1. Using the 3-step rule, find ƒ' (t) given f (t)= 2t+1 t+3

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Q: 10) Given the functions f(x) = 4x² - 5 and g(x)= 15-3x, find (fog)(4). 4 (15-3X2-5 Inverse:…

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Q: Factor 1296x4-14641 and solve the equation 1296x4-14641 = 0

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Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: 1. Let R be the region bounded by y = x² and y = 6x - 8. Find the volume of the solid S generated…

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Q: Check Your Understanding: Why is it not always necessary to use the quotient rule to find the…

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Q: −|x\, x≤-5 h(x) = {20 − x², −53

A: Given dataA function,

Q: Consider the points P(2,2,4) and Q(10,8,8). a. Find PQ and state your answer in two forms: (a, b, c)…

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