Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis. y=3x1/2 , y=0.4x, and x=4. Round off only on the final answer expressed in 3 decimal places.

Q: Find the derivatives of the following Trigonometric Functions and Inverse Trigonometric Functions:

A: y = ex sin-1xdydx = ex ddx(sin-1x) + sin-1x ddx(ex)        = ex 11-x2 + ex sin-1x 

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A: Given:  Statement: To determine whether a given series converges, it is important to first consider ...

Q: solve

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Q: Let f be the function given by f (x) = sin(2x) cos(1 +x). What is the average value of fon the close...

A: Given function f(x)=sin(2x) cos(1+x)       ; 1≤x≤3 use the formula 2 sin A cos B = sin(A+B)+sin(A-B)

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A: Given :∫1x2-6x+bdxTo find :  How could I calculate the b value using u-substitution and partial frac...

Q: Find the derivative of the following functions: = Arccos 4x -4 ans. y' = V1-16x2 4. y = Arcsec(sec 2...

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: 14. у %3D Sin-1 (Зх - 1) -3 3 Od. T-9x +6x Зх-1 O0. -9x+6x OCT-9x+6x Oa. V1-(3x-1)

A: Let's find. 

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x³ - 3x? + 4x- 12 2...

A: y = x3 - 3x2 + 4x - 12y = x2(x -3) + 4(x - 3)y = (x2+4)(x - 3)   X-intercept: (3, 0)    [Real values...

Q: For Nos. 9-10: Suppose f is a function such that f0(5) is undefined. Which of the following statemen...

A: Given that a function f is as follows  I.e f(5) is not defined  We know that  Any function is contin...

Q: Consider the parabola given by y = x² + 1. a) Use Lagrange's method to find the point on the parabol...

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Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves...

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Q: From a point A the angle of elevation of a mountain is 13.7°, and from a point B, directly behind A,...

A: Given query is to find the height of the mountain.

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Q: Calculate the indefinite integral 6dy 25 –9y2 -

A: Given: ∫6dy25-9y2

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Q: (Don't forget to include the constant of da x + 3 antidifferentiation C) Evaluate

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Q: (x+2)? dy 2y dx x -4 x² -4

A:    dydx+2yx2-4=x+22x2-4⇒dydx+2yx2-4=x+2x-2⇒y=∫x+2x-2dxx+2x-2x-2

Q: x+2 3. y = ( X-2 at x = 1

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Q: 3 x2 If f(x) find: 8+ x2 f'(x) = %3D

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Q: When you evaluate: dx. The sum of the coefficient of X" for any constant n> 0 is. A None of the give...

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Q: The furnace in a home consumes heating oil during a particular month at a rate modeled by the functi...

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Q: 5-8 Find an equation of the tangent line to the curve at the given point. 5. y = 4x - 3x², (2, -4) 6...

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Q: Match the function on the left to its appropriate antiderivative on the right. Prompts Submitted Ans...

A: Top two are the identities of anti-derivative. I have solved the last one properly and wrote the dir...

Q: Which one represents the area of the shaded region?

A: The standard formula to calculate the area between two curves is given as follows: If P : y = f(x) a...

Q: Given the cost function, C(q) = q³ – 30q² + 7200q, Obtain the marginal cost function and determine t...

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Q: 100 500 2500 20 Given the series 9 81 729 6561 Does this series converge or diverge? O converges O d...

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Q: sinh(2 In(c)) = %3D (A) 을 + 늪 2c (B) c² – (C) 를. -옮 (D) c- (E) 0

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Q: Select all statements that are true. If f is continuous everywhere except at x = 0, then lim t→0- | ...

A: This is a question related series calculations. If it leads to the particular value then it is conve...

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: 2. (cos"B- sin4 ß )?dB

A: ∫cos4β-sin4β2dβ∫(cos2β)2-(sin2β)22dβ∫(cos2β-sin2β)(cos2β+sin2β)2dβ∫(cos2β-sin2β)(1)2dβ∫cos2β2dβ     ...

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Q: Find the derivatives of the following Trigonometric Functions AND Inverse Trigonometric Functions: 9...

A: Let's find. 

Q: If > uk and > v% are convergent series, then > (uk + v%) and 2(uk – Vk) are convergent series and th...

A: First we take partially fraction then we use sum of GP. 

Q: 11. y x Sin x + (1 -x) Cos x Oa. x Sin x+ 2x Cos x b.x² Sin x ©* Sin x dxSin x+ 2 Sin x

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Q: 9. (b + 4)e db

A: This question is based on Indefinite integration.

Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (1, -4) and the direction in w...

A: Here, the given function is: f(x,y)=ln(x2+y2)

Q: 4. y² +2xy = x+y

A: We know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Quotient rule: fg'=f'·...

Q: (e*+ y)dx + ( 2+ x + ye )dy =0

A: Given, (ex+y)dx+(2+x+yey)dy=0 expand the terms to get the solution Note: xdy+ydx = d(xy)

Q: dy = ay + b whose dt Write down a differential equation of the form all other solutions diverge from...

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Q: 20/40) ty' + (t + 1)y = t, y(ln 2) = 1, t >0

A: Given, ty'+(t+1)y=t And initial condition y(ln2)=1

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x³-5x)* 1. у3D ; d'y/dx³

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Q: Question 5. , Which of the following statements is true about the lines L1 : x= 4 – 2t, y = 2+ 2t, z...

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Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans ...

A: The given equation is P(x) = -0.001x^2+5x-1875. We have to find maximum value of P(x) ( profit). Cle...

Q: 1. Given the vector-valued for R(t) = (2 sin 2t – 1)î + 2 cos 2tj + 3tk. (a) Find the length of the ...

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Q: Find 02/ay and az az 02/ax of the following function: z = x³ev* + y5 In(2x + y)

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Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of...

A: Let the length of the rectangle be:  l  cm Let the width of the rectangle be:  w  cm

Q: For each given combination of values of lim f(x) and f(c), sketch the graph of a possible ズ→C functi...

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Q: y + Jx² +y2 dx = xdy when x-3', y=l 4. %3D

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