Direction: Eliminate the following arbitrary constants to obtain the DE. 5. x = c1coswt + c2 sinwt

Q: A solid spherical steel ball, 20 cm in diameter, is placed into a tall vertical cylinder containing…

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Q: Find the value of x for which the value of the function f(x) = x +3x2 - 2 is minimum? %3D Answer:…

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Q: g(x) = e× In x12 g'(x)=

A: topic - derivative of a function

Q: Differentiate. f(x) = e 13x f'(x) = |

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Q: Derivatives of trigonometric functions Find the derivative. 1. y = 3sin x +3 cos x - tan x

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Q: Consider the function y = 5x4-4x3-3x2+8x-12. What is the average value of the function on [-3, 1] ?

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Q: EXACT VALUE OF C IN INTERVALS QUESTIONS (such that f(c) = fave) A. 3x2+2x - 4, [-2, 4]  B. 5cos(x)…

A: As per our guidelines we are supposed to answer 3 sub-parts , kindly repost the remaining part as…

Q: Find Ay and f'(x)Ax for y = f(x) = 2x – 1, x= 3, and Ax = 3. Ay = (Round to four decimal places as…

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Q: A function f(x) passes through the points (15,24), (18,37), and (22,25). Use the Lagrange Formula to…

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Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

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Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is…

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Q: A company has identified that the revenue R for a particular product is given by the function f(x) =…

A: Solution is here

Q: 7. (D+ 3)'y = 15x'e-3* 8. (D- 4)'y 15x²e**. 9. D (D – 2)²y = 16e2 10. D2(D + 3)²y = 9e-3x 11. (D² –…

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Q: The barrel of a fountain-pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel…

A: Given that the fountain pen barrel is cylindrical in shape.

Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

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Q: Which of the following is equivalent to cos 0? cos 0(1+ tan? 0) sin 0 + tan 0 1+ sec 0 O Option 1 O…

A: Checking all options by simplifying.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 5, -1) Vw(9, 5, -1) =

A: Explained below

Q: (b) If a > b and c > 0, then ac > bc.

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Q: Given than | f(x) dæ = 4 and f (x) da 8, which of the 3 following is NOT TRUE?

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Q: Note: you will need to find both the gener e homogeneous problem, and a particular so mogeneous…

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Q: | sin'x sin 2x dx

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Q: 7y" - 18y %D

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Q: Let f be a continuous function on [a, b]. Which of the following statements is false A If k is a…

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Q: 2) y TC cos 30 1 b: Period: a: d: Phase Shift: C:

A: We have to find a,b,c,d, period and phase shift.

Q: y dy J 725 – 16y 2.

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Q: s the volume of the frustum of a cone whose upper base is 16 cm in er, lower base 10 cmin diameter,…

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Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: Which of the following is equivalent to cos (60° + 0) + sin(30° + 0)? cos 0 + v3 stn e cos e O…

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Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: Find the maximum value of the function f(x) x - 9x2 + 15x- 5.

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: For orthogonal trajectory we replace dy/dy by -dx/dy

Q: Determine whether the planes are parallel, orthogonal, or neither. 4x – 20y – 4z = 4 3x – 15y – 3z =…

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Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: 2x

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Q: If a cylinder, a hemisphere and a cone stand on equal bases and have the same heights, what will be…

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Q: Where is the function decreasing? * (-1,3) (-2,1) (0,1) O (*-1) O (*, *) O (-1, ) O (-*, 3)

A: A function is said to be decreasing in an interval in which on increasing the value of x, the value…

Q: is given by: If f(x, y) then 8(8x-4y) '

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Q: Consider a right pyramid whose base is an equilateral triangle of side 4 cm each. If each slant edge…

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Q: 11 2

A: We can solve this as follows:

Q: Question x2+4 Using Partial Fraction Method, evaluate: S x(x+2)(3x-2) Your answer

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Q: Find the general solution for the following equation: y''' + 3y'' – 4y' – 12y = 0

A: Solve the differential equation by assuming eλx for some constant λ.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Consider the following. x = 4 sin(80), y = 4 cos(80), 0sos (a) Eliminate the parameter to find a…

A: Solution: x=4 sin (8θ)y=4 cos(8θ)  ,     0≤θ≤π4 Let 8θ =t  So,   0≤θ≤π4 multiplying by 80≤8θ≤8π4…

Q: Find the volume of the region lying above the cone o = and below the sphere p = 7. (Use symbolic…

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

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Q: ) Given the following derivative function 2x – 5 f'(r) = Þ – I^ what are the critical numbers of…

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