Find the general solution of * 4y - 23y" - 33y" - 17y' - 3y = 0

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A: From chain rule  If g(x) is a differentiable function, then the derivative of eg(x) is g'(x)*eg(x) ....

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Q: If f(r) 2x(sin z + cos ), find f'(z). f'(#)- Evaluate the derivative at a = 3. Enter an approximatio...

A: Given query is to find the derivative of the expression.

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A:  w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

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Q: Verify that the area under the curve y = 1/x from x = 1 to x = m equals 2m, the area from x = 3 to x...

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A: V(t) = d[x(t)]/dt Put, v(t) > 0.

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Q: 1. Given : %3D 13 4 -6 -4 4 A = 24 4 12 2 8 - S 4 6. 3 2.

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Q: Derive the following formulas using the technique of integration by parts. Assume that n is a positi...

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Q: 2t – 3t2 | (c) h(t) %3D a = 1 1 + t³

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Q: Let each of the vectors A = 5a, -- a, + 3n,, B = – 2a, + 2a, + 4a,, and C - 3a, – 4a, extend outward...

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Q: given

A: We will solve the integration. 

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Q: q7

A: We will solve the Differential equation. 

Q: Find the sum of the infinite series, if it exists. -16 -64 32 8, , 5, 27· 3 Enter the sum as a fract...

A: The given infinite series,8, -163, 329, -6427,.......

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Q: Find the integral. e4X cos 3x dx + C

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Q: What is the antiderivative of -dx? A 6x2 1/3 + C ® x/3 (2x% +9) + c %% + 6r/2 + c /2+c

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Q: driver driving along a highway at a steady 41 mph (60 f/sec) sees an accident ahead and slams on the...

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Q: 10. y(2x3 -x?y + y³)dx - x(2x³ + y³ )dy = 0

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Q: Use algebra to simplify the expression before evaluating the limit. In particular, factor the highes...

A: Our Aim is to evaluate the limit of the expression given below:-limn→∞2+8n+7n26n2-5n+7 -(i)

Q: The graphs of the first and second derivatives of a function y = f(x) are shown to the right. Sketch...

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Q: Evaluate the integral below along the given path. (Give your answer correct to 2 decimal places.) C:...

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Q: Determine the equation of the curve whose tangent line at any point (x, y) is e* - cos x and passes ...

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Q: On which interval does the function f(x) = (x+ 5)/(x - 1) discontinuous? %3D O a. (1, 2) O b. (-2, 1...

A: topic - limits and continuity

Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point P...

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt; ...

Q: The height (feet) of an object moving vertically is given by s = - 16t2 + 144t + 108, where t is in ...

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Q: -32 2dy = 0

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Q: Given the differential equation y" - 6 y' = 0 Determine the Characteristic Equation for the Differen...

A: First we find out the characteristic equation of the given differential equation.

Q: (vz-i, »). a Let 7(t) = (/2-i -1+e' In(t + 1) (i) The domain of 7 is [a] (input a number from below)...

A: The domain of a vector function is the set of all t for which all the components of vector are defin...

Q: find the constant term of (2x² + 1/x)⁹

A: find the constant term of (2x² + 1/x)⁹