Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement.  f(x) = x2 − 3;   [3, 5]

Q: The graph below is the function f(x) -5-4-3 -2 5 4 3 4 F-2 -2 -3 -4 Select all statements below that…

A: Here we have to choose the correct options.

Q: 2. Express the rational function as a sum or difference of two simpler rational expressions. (Note:…

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Q: Question 6 Is the differential equation y2dx + 2xydy=0 exact? A YES B) NO

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Q: Consider a particle moving along a curve so that it is at position f(t) = (2+³, 2+²) at time t. Then…

A: Given :ft=<2t3, 2t2>The particle is moving parallel to <1,-2> at time t

Q: Q1 02 Q3 04 05 Q6 Q7 Q8 The trigonometric substitation to evaluate the integral (√16-dx in A)x=4sing…

A: Let's solve for infinite series sum.

Q: Question 9 Which is equivalent to Inlyl=3x + Cwhen y is solved in terms of x? A B y=ce²x y = 3x + C…

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Q: y't y X -0 ✓g (0) =) J

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Q: x x + x = 0 x + x 3

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Q: 1 7. f(x) = √√√1 + √1 - x, at x = ² 4

A: Chain rule of differentiation is used.

Q: Two straight line are y = x -1 and y = -x + 1. Find the point of intersection: i) using Cramer's…

A: We can solve this as follows:

Q: 1. y = 7-x² + 4x³, at x = -1 2. f(x) = x³ = 5x + 4, at x = 1 x 2 x²+4' at x = 2 3. y =

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Q: Q12 Find (3 in)) is: A)-300) sin(x) B) 3x) cosx ln(3) C)-3(3) sin(x) D) 3

A: 12). The given function is; fx=3sinx   As we know the Chain rule: fgx'=f'gx·g'x And the common…

Q: y = x²+4' at x = 2

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Q: (D³5D² + 17D-13)y=0; y(0) = -1, y'(0) = -4;y" (0) = 17 ubstitution and Elimination in Finding the…

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Q: I need the correct answer for all of them please.

A: Here we have to find the local and absolute extrema.

Q: 1. Sketch the graph of the function -1, f(x) = √25-x², (x - 5, x ≤-5 -5 < x < 5 x ≥ 5

A: We have to sketch the graph of the function.

Q: Evaluate the limits as a goes to infinity. (a) lim 5+6+7z² 2+4x²+8x³ 818

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Q: What is the general solution of the differential equation y"-2y'+y=0? Ay=C₂₁e²*+C₁₂xet (B) There is…

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Q: 10. Find the area bounded by the curve y = 2x² and the lines y = 0, y = x, x = 2.

A: Let's find area bounded by the curve.

Q: .Identify the values of a, b, and a that could be used with the quadratic formula to solve the…

A: 2.

Q: The curve y²-x²= -5x is a solution to the differential equation y = (2x - 5)/2y (A) TRUE B) FALSE

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Q: b/ by using Chain Rule, the derivative of - sin 2t) is g(t) = tan (5

A: Solution

Q: Please ans 2

A: Topic:- function

Q: x + y + z x+y=4z = -4x+y+ z LO 5 10 0

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Q: If lim X-5 f(x) - 4 X-4 = 3, find lim f(x). X-5

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Q: Solve the differential equation A) Iny-x=C B) Iny=c C) x + In y = C D) In c-y = x dy dx =y

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Q: NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of…

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Q: 4) w(x) = -3x - 4; Find w(7) 4-2, Find 6) g(n)=n² + 2; Find g(3)

A: (4) The function is given by wx = -3x-4 6) The function is given by gn = n2+2 To evaluate: The value…

Q: rob 2 Evaluate lim (√92² +2² - 32) 846

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: 4. For each of the following polynomial equations, determine if x = 1 is a root. (a) x³2x²-3x-2=0…

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Q: e√x, at x = e 9. y = e√x,

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: 3 tanx-2xy = c

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Q: In Problems 7-10, xc₁ cost + co sin t is a two-parameter family of solutions of the second-order DE…

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Q: Show that the equation represents a circle by rewriting it in standard form. x² + y² + x = 0 Find…

A: Please see the below picture for detailed solution.

Q: Can you please provide a graph

A: We can draw the graph .

Q: 0=8-1号-25号+ex (2)

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Q: 5. This rectangle of x's is of another (original) rectangle of x's. X X X X X X X X X X Show the…

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Q: y=Get+Cocos x + C3 sinx

A: Since in this equation there are three arbitrary constant so differential equations is of order 3.

Q: Use integration by parts to find the following: [(t+ 7)e²²+3 dt = | 2t+3 t=+C

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Q: The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. 1 2 8…

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Q: Find the perimeter and area of th rectangle that is 4 m * 0.5m

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Q: b/ For the following function the range is y = √4-x

A: We have to determine range

Q: 4. y = x(x+1) 2x-1 at x = = 0.6

A: We can find the slope as below.

Q: 5. Compute the area bounded by the curve x = 1/y, the line x = 6, 2x - y = 0 and y = 0.

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Q: Q16 Find of y-In(In(e)) A))))

A: 16)y=ln(ln(ex)).

Q: Eliminate the constant: =c₁e²x+c₂e³ 3x

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Q: y" + 20y' + 64y = 60e-4x

A: To find the solution

Q: (b) lim 4-5x²+2x 3x³-2x+4 848

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Q: 05 Q6 A) Which of the following seri 1) C) 1 D) diverge D) 1

A: We need to find summation.

Q: Sketch the graph of the function by first making a table of values. k(x) = ³√/-x X -27 -8 -1 0 1 8…

A: Let's sketch the graph of given function.