Evaluate. da [3.sin x] O x 3-¹ (sin x + cos x) O 3 In 3 cos x ● O 3. cos x 3 cos x + 3* .

Q: A company buys a machine for $475,000 that depreciates at a rate of 30% per year. Find a formula for…

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Q: Given the differential equation (x2 y2+ x2 + y2 + 1) dx + x2 dy = 0 with the condition y(1) = 1:…

A: Given the differential equation x2y2+x2+y2+1 dx+x2 dy=0 with the condition y1=1.1 To identify…

Q: Differentiate using first principles. f(x) = -3x² + 4x+6

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Q: Problem 2: Given the differential equation (y sin x - cos²x) dx + cos x dy = 0: a. Identify whether…

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Q: Find y' and y" for x² + 2xy - 3y2 = 41. Simplif

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Q: For the problem below, is a central angle in a circle of radius r. Find the length of arc s cut off…

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Q: (ex-y + 1) dx- (ey + ex-y) dy = 0: Show if it is exact, variable-separable, or first-order Give the…

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Q: A tank initially contains 106 m³ of a bleach solution with 5 grams dissolved chlorine. Fresh water…

A: Let x be the amount of chlorine=x grams and x0=5 grams

Q: Experiments show that a colony of bacteria with sufficient food and no predators and with zero death…

A: dPdt=kP given P(0) =P0 = 44837

Q: 5. Find the derivative of each of the following functions. Simplify where possible. x a) f(x) =…

A: See this solution in below.

Q: 8. Find the equation of the line that passes through points C(-2. 1) and D(2, -3).

A: eouation of line passes through two points (x1, y1) and ( x2,y2) is given by  y - y1 =y2 -y1x2-x1(x…

Q: (xy + x + y + 1) dx + y dy = 0 Where: . . y(1) = 0: Check if it is separable, exact, or linear. Give…

A: See the details solution in below

Q: Solve for the relative min value of y = 14x - 4 In (3x)

A: The function is given by y = 14x-4ln3x To evaluate: The relative minimum value of the function.…

Q: If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the…

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Q: Solve for the min value of f(x) = 5x² + 4x + 6

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Q: 227. y' = 3x + xy

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

A: We need to find out the average value of the function.

Q: Let f(x) = e+ln x x2 . a. Find the average rate of change of f(x) from x = 1 to x = e. b. Write an…

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Q: Compute the area of the region enclosed by the y-axis and the curve in the xy-plane given by the…

A: Given parametric equations x(t) = t2 − 6t  and  y(t)=10t3 + 9t

Q: Find the indefinite integral. (Use C for the constant of integratio t [F:8* dt + 81 X

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Q: Consider the function y = 2- 8x + 6 on the interval 8x² a) Find the slope of the secant line on this…

A: The given function is; y=sqrt(8x2-8x+6), [-3/2,5/2].

Q: Determine whether the lines L₁: F(t)= (0, 1, 1)t + (-3,- 2, 3) and L2: p(s) (3, 1, 2) s + (-6, -6,4)…

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Q: I 3х x+4 -dx

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Q: 2. Form a polynomial f(x) of least degree having real coefficients, i as a simple root, 0 as a root…

A: We have to form a polynomial f(x) of least degree having real coefficients, i as a simple root, 0 as…

Q: Simplify the difference quotients when necessary. 9) f(x) = 7x + 1 A) 7x - 7h; 7x - 7a f(x+h)-f(x) h…

A: Given query is to perform indicated operation on the function.

Q: 2. Use Root Test to determine whether the series ally converges, or diverges. +∞ n=1 (-1)" (sin())"…

A: Given series is ∑n=1+∞-1nsin1nnnn. We need to determine whether the given series is absolutely…

Q: If f(8)=4, f'(8)=-5, g(8)=-3, and g'(8)=1 and h(x)=6f(x)-2g(x) find h'(8)   a) -32 b) -114 c) 0…

A: h(x)=6f(x)-2g(x) h'(x)=6f'(x)-2g'(x)

Q: Given the differential equation (xy + x + y + 1)dx + xdy = 0 that has a condition of y(ln2) = 0 b.…

A: given differential equation is solution below.

Q: Let f(x) = x¹ +5x³-792²-137x+66 be the function graphed here. Click on the graph and expand window…

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Q: Use the method of reduction of order to find a second linearly independent solution 32 (a) (b) x²y"…

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by x2 compare this DE…

Q: Problem 2: Given the differential equation (2xy - elnx-x²) dx + dy = 0: a. Identify whether the…

A: Given the differential equation 2xy-eln x-x2 dx+dy=0:a To identify whether the differential equation…

Q: Let y = 2x². Find the change in y, Ay when x = 5 and Ax = 0.3 Find the differential dy when x = 5…

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Q: 1 sin x x² dx

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Q: Find an equation of the tangent line to the curve at the given point. y = 5e + x, (0,5) y =

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Q: Find the intervals on which f is increasing and decreasing. Зл Зл f(x)=7 cos (5x) on Select the…

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Q: 3. Find the average value of the function f(x) = tan³(x) sec²(x) on the interval [0]

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Q: (1, √3) (a, b) = (-2, (-2,√3) (2√3, 2) (√3, 1) (√3, -1) - (a, b) - (a, b) = - (a, b) = (-1, √3) (a,…

A: Given query is to find the Cartesian coordinates of the point P.

Q: Find Position, Velocity and Acceleration Vectors Find the position vector for a particle with…

A: Concept: The formulas used v(t)=∫a(t)dtr(t)=∫v(t) Also the integration of xn is ∫xn=xn+1n+1+C Where…

Q: Find the linear speed of a point moving with uniform circular motion, if the point covers a…

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Q: For the function defined below, find all values of x and y such that both fx (x,y) = 0 and fy (x,y)…

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Q: 23. Find a formula for the inverse function f-¹ of f(x) = 9x+6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: x" - 16x = 4 sin(2t) with IC x(0) = 1 and x'(0) = 6. Find x(0.25) to at least 3 decimal places of…

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Q: Use the quotient rule to find the derivative of 4x³ 5x³ 4x4

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

Q: Given that  f(x)=x^9h(x) h(-1)= 3 h'(-1)=6  calculate f'(-1)

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Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 2x² + 5y² = Please show…

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Q: Find r(t) and the velocity vector v(t) given the acceleration vector a(t) = (8e¹, 16t, 14t + 4), the…

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Q: Find the exact length of the curve: y = 10 + 1 6x3, 2 ≤x≤5.

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A: By using the shell method to set up and to evaluate the integral that gives the volume of the solid…