Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U x² Edit Insert

Q: Consider y=√x+1. (a) Find its inverse relation. Is this relation a function? Why? If the inverse is…

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Q: 1. Carbon 14 is a common form of carbon which decays over time. The initial amount of carbon 14…

A: Please see the below pictures for detailed solution.

Q: 1. A 6 kg sign is suspended by two strings making angles with the ceiling as shown in the diagram.…

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Q: (iii) Find the total area of the following shape PQRS. (You may need a calculator) 7cm 12pt…

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Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

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Q: The function f(x) = x³ + 7x² + 7x − 25 is graphed below. Plot a line segment connecting the points…

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Q: A y 10+ -10-8 -6-4 -2 8 9 2 2 7 6 8 -10- 2 45 8~9 10 X

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Q: A1. SOLVE STEP BY STEP IN DIGITAL FORMAT Using the following function and the given intervals…

A: Given - f(x) = 4x^2 - 6                [ 3 , 6 ] ∆y/∆t =[ f(X2) - f(X1) ] / ( x2 - X1)

Q: 1. Find the area under one arch of the curve y = cos- :cosex.

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Q: (-1,1) a N (1,1) 2

A: find the domain and range of the given graph Domain: set of x values for given function Range : set…

Q: egrate the following by hand, shc 9 (a) 3 3 √x³ - 24+8) dx

A: We can solve this as follows:

Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: from X-TT to x=3TT/2

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Q: 1. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in…

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Q: = 4) Use the recursion formula Stan" xdx to calculate Stan³xdx tan" X n-1 n-1 -ftan”-2 xdx

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Q: Find the direction vector of the line which is the intersection of the planes x + y + z = 1 and…

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

Q: 10 times as many as 1 hundred is_______ hundreds or ________ thousand

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Q: For the function y = f(x) = 3x³ – 10: df dx a. Find ƒ'( − 2) b. Find a formula for x = f-1(y).…

A: NOTE- "Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: −5x – 5, f(x) = 2x² + 2x - 1, x < -1 x ≥ −1

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Q: Express the rule in function notation. (for example the rule “square, the subtract 5”is expressed as…

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Q: EX #3: Roller Coaster A hypercoaster is a special circuit roller coaster with a height measuring…

A: A hypercoaster is a special circuit roller coaster  with a height measuring greater than 200 feet.…

Q: Find the derivative of ( Ⓒ) (05'(x)

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Q: Use the matrices below to perform matrix multiplication. B If the operation is undefined, enter NA.…

A: Please see the below picture for detailed solution.

Q: 0.5 for A mortality table is defined such that¸p¸ ={1— x100. Calculate the complete expectation of…

A: Answer is 40.

Q: = $r(t)dt 5. Use the graph of f(t) = 2t - 5 on the interval [-2, 10] to write the function F(x),…

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Q: Define g(x) to be the restriction of f(x) to the largest possible domain containing x=0 so that g(x)…

A: We have given f(x)=x-12+2You asked to solve only part(b). So we will solve part(b)In part(b) we have…

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

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Q: limr→(1 − )tan =N x

A: Concept: Limit of a function: Think about the f function (x). X must have values ​​close to the…

Q: Given r(t) = 9t² i + 18tj and t = 1, find the tangential and normal components of acceleration. ат…

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Q: Let y = tan(2x + 2). Find the differential dy when z = 5 and dr = 0.2 Find the differential dy when…

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Q: For the function f(x) shown below, determine lim f(x). f(x) = x² - 10 -3 - 2x for for +-←æ x -4

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Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: Find the curvature (t) of the curve r(t) = (−4 sin t) i + (−4 sin t)j + (1 cost) k

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Q: If {an} and {bn} are divergent, then {an bn} is divergent. Select one: O True O False

A: The objective of the question is determine the choosing the correct option.

Q: 7 Write a limit using summations that would equal S Answer: lim N→∞ n k=1 [x³ - 4] dx. Submi

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Q: Find the inflexion point(s) of f(x) = x²-3x²³

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Q: The graph of y=f(x) is shown below. Find the values of f(x) for x=0,x=3 and x=6

A: Here we have to find the values of f(x).

Q: 9. Given vectors = [3,-6,8] and v= [4,-2,-5], determine uxv.

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Q: A wooden artifact from an ancient tomb contains 60 percent of the carbon-14 that is present in…

A: Please refer to the image below

Q: If what does the following integral equal? 4 1₂ 3 h(v)dv= 9 [h(v)dv = 15 - 3 and 9 Ione h(v)dv= = =…

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Q: 2x e²x cos(y)dx + e* sin(y)dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: 19. 2x³y = y(y² + 3x²).

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Q: f(x) = -2x² + 7 7x 10 - if x ≤ −1 if x > -1

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Q: Sketch the region enclosed by y = 7x and y = 9x². Find the area of the region.

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Q: Given |F₁ = 85 N and |F₂| = 125 N and they are acting at an angle of 14 a) Find the magnitude of the…

A: Topic:- application of vector algebra and trigonometry

Q: Determine it each of the following is absolutely convergent, Conditionally convergent, for…

A: We have to test whether the series is absolutely convergent conditionally convergent or Divergent.

Q: X 2 Find x² +1 -dx

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: Given: The depth function: D(t) = 2sinπ4t+5π4+5 Depth is changing at 6 a.m. t = 6

Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: 3. f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below…

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