Find f(x) if y = f(x) satisfies dy dx 80yx⁹ and the y-intercept of the curve y = f(x) is 6. f(x) =

Q: Question 6 Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0…

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Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

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Q: If f(x) f'(x) = [ 7-x² 3+x² find:

A: Topic = Derivative

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: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: 7rer dr =

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Q: Is the following piecewise function continuous? if x < 0 0<if x < 3 if 3 < x f(x) = -3x² x - 3, . -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: EQUATIONS 5y" - (y) = y³ sin æ 4 x yy" + 2x = tan x ºr + (5) - w = 4et St2 88 SM - (SM) dy³ xt' +…

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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: 150 5 -4 -2 100 50 -50 -100 -150 200! 2 4 6 8 Xx

A: We know that, The highest point the graph ever reaches is the absolute maximum. The lowest point the…

Q: Find the indefinite integral and check your result by differentiation. (Use C for the const (x³ -…

A: The given integral is ∫x3-12x-4dx use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C use the…

Q: 6)Find the first quadrant area of the region bounded by curves defined by given equations

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Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

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Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

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Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: The given sum is ∑i=164i+5

Q: 1. A rectangle has a perimeter of 14 m. Express the area of the rectangle as a function of the…

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Q: - п/2 эт/2 п/2 0 п/2 3г/2 5г/2

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Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

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Q: Find the radius of convergence, R, of the series. R = 00 I = n = 1 xn n45n Find the interval, I, of…

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Q: Question 5 (i) Use the diagram below to find sin(0), cos(0) and tan(0). (ii) If sin (500) -1…

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Q: Given the function f(x)= |x-1|: (a) explain why f(x)= |x-1| does not have an inverse function over…

A: Given fx=x-1

Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: A particle moves along the x-axis so that its position at time 0 ≤ t ≤ 18 is given by x(t), whose…

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Q: A cylindrical can without a top is made to contain 10,000 cubic cm of liquid. Find the dimensions…

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Q: 10 5 f(x) 10 5 10 10 X

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Q: Given the function f(x) = −4 sin³ x, find ƒ'(x).

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Q: Calculate S√4-x² dx

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Q: 3. State the components of a unit vector that is perpendicular to the vector =(5,2,-1).

A: To state the components of a unit vector that is perpendicular to the below vector v. v=5, 2, −1

Q: Obtain the General Solution of the following differential equations. 1. x²y y' = ey 2. (xy + x)dx =…

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Q: A manufacturer can produce 2700 cell phones when a dollars is spent on labor and y dollars is spent…

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Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: Suppose p′(−1)=−2 and q′(−1)=−5.5.  If r(x)=−7p(x)+10q(x), find r′(−1).

A: We have to find the value of r'(-1).

Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

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Q: Evaluate the indefinite integral sin² t cos³ tdt = + C

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Q: 13. A radioactive isotope has half-life of 43 days. What percent of the original amount remains…

A: Topic:- application of algebra

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: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: Given that answer= 5 f(x) dx = 3' what is 11 f(w)dw?

A: Property of Integral : 1.∫abf(x)dx=I ⇒ ∫abf(w)dw=I   2.∫abf(x)dx=I ⇒ ∫baf(x)dx=-I

Q: The following table shows the rate of water flow (in L/min) through a dam. 1 5 9 13 17 21 25 t (min)…

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Q: 1. (x³ + xy²)y' = y³ Ssangen job10 2. (2x + y)dx= xdy 3. x³y' + x²y-y²= 2x4

A: Topic:- differential equation     Definition:- The order of a differential equation is defined to be…

Q: lim 2-0 |3x-1| + 3x + 1| I

A: Given problem :- limx→03x-1+3x+1x

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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Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

A: Here is the solution:

Q: Explain why the integral is an improper integral and evaluate it: =dx √x-2

A: Given integral:- ∫251x-2dx

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

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Q: the interval that f(c) = k. there exists a value c, where <C Must there exist a value of c in the…

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Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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Q: Find the value of C so that y(t) = Ce2t satisfies the initial condition y(1)=1

A: Substitute t=1

Q: h. Use the second derivative to identify intervals where f(x) is concave up. (-0,3) X i. Use the…

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