Use the General Power Rule to find the derivative of the function. g(x) = 4/(6x2 + 5x)9

Q: . The function f(x, y)= 8x' - /4x* + 3y* is homogenous in x and y of degree -. The function f(x, y)=...

A: Here we have to find the degree of homogeneous function

Q: Let an be then th digit after the decimal point in 3T + 7e. Evaluate Ean(-1)". n=1

A: This is a problem related to sequence and series part. based on the general formula available for ge...

Q: 2. x'dy+(2ty– y°l&x =0 Let the substitution y=²; y=vx; dy=vdx+ xdv

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

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Q: Part 1. Setup the integral that will give the mass of a metal rod that is 1l inches long (orientated...

A: length ofrod = 1 inches density of rod ρ=4x lb/in

Q: Find the orthogonal trajectories of the family of circles through the origin with centers on x axis.

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Q: x^2y=4+Cy Eliminate Arbitrary Constant

A: Here we will eliminate arbitrary constant,  

Q: 1 A water tank has the shape obtained by rotating the parabola y equals x squared about the y-axis, ...

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Q: Spot the mistake/s in the solution. Tick the box that applies. CSC csc" da -2 dx 3 S cccx cot x dx *...

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Q: yesin 3y* dy dy 5. csc 6y

A: The question is a little incorrect. I have modified the question a bit: the denominator should be: c...

Q: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z? ...

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Q: x- 1 (i) y = () y = Vx(Vx+1) x + 1

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Q: S In²sinx -dx , the integrand is In the expression /= tanx Insinx A tanx B -Insin3x+C 3 In?sinx tanx...

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Q: Evaluate whether the following initial values is true in the function: y=4cos(x/2)+3x² a.) when x = ...

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Q: Solve the following second-order differential equation: yn+ 4y'+ 5y = 8x sin x

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Q: Prove the identity 1÷(1-sinx) =sec^2 x +tanx secx

A: 1(1-sinx)=sec2x+tanxsecx

Q: 1. y’dx-(xy+ y² kdy = 0 Let the substitution y=2; y=vx; dy=vdx + xdv

A: Given that: y2dx-(xy+y2)dy=0

Q: Find the orthogonal trajectories of the family of ellipses with centers at (0, 0) and two vertices a...

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Q: d the area (sq. units) covered by the line 2y = x + 6 from x1 = -8 to x2 = 0.

A: Given query is to find the area bounded by the curve.

Q: Evaluate the definite integrals using properties of the definite integral and the fact that 4. 4 Lfe...

A: given : ∫-52f(x)dx=-3 , ∫24f(x)dx=8 , ∫24g(x)dx=8(a) ∫-5210f(x)dx=10∫-52f(x)dx=10×(-3)=-30 ∫-5210f(x...

Q: The demand function for a company's product is p 24e-0.99 where g is measured in thousands of units ...

A: Given: p=24e-0.9q  

Q: All parts of this problem refer to the function below. y = (9+ 6x)²/¤ dy a) Use logarithmic differen...

A: We have to find derivative

Q: x'dy+ (2xy – y° ktx = 0 2. Let the substitution y=2; y = vx; dy=vdx+ xdv y

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Q: Find an equation of the line tangent to the graph of G(x) = 7 e -5x at the point (0,7). The equation...

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Q: 1.)(x + 2) * t * a * n * y * d * x + (x ^ 2 - 2) * csc(y) * d * y = 0 2.)(y ^ 2 - xy) * d * x + (xy ...

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Q: A car is travelling at 72 km/hr. At a certain instant its brakes are applied to produce a constant d...

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Q: Expand the expression. If possible, write your answer without exponents. 4. X, - 5 log 5 3+x² x-5 lo...

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Q: Cora baked 16 cookies with 2 scoops of flour. With 5 scoops of flour, how many cookies ca Cora bake?...

A: Cora baked 16 cookies with 2 scoop of flour. With 5 scoop of flour, how many cookies Cora can bake.

Q: Integrate the rational function by partial fraction (decomposition): 2-9-dx r3-9x

A: Let I=∫x2-9x-9x3-9xdxApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdxI=∫x2x3-9xdx-∫9xx3-9xdx-∫9x3-9xdxI=∫x2...

Q: If y=3(−7x^2+7x+1)^13, then      dy/dx=

A: Given:- y= 3(-7x2+7x+1)13 To find :- dy/dx

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: topic - application of derivatives

Q: Find the DE of each of the following by eliminating the arbitrary constants. y =Ce* +C2cos.x +C3sin ...

A: Herw we have to find the differential equation.

Q: 1. y'dx-(ty+ y*Jdy = 0 Let the substitution y=2; y=vx; dy=vdx+ xdv

A: Given:

Q: Write an expression for the distance w in terms of y. Simplify your answer and write the terms in de...

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Q: If the limit of a function f at x-3 equals -4, then which of the following are true?

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Q: sin² 3y 5. ye 3^cot3t

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Q: Calculate the derivative 33 4:6 dx using Part 2 of the Fundamental Theorem of Calculus. 33 dt = da

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Q: Find the derivative of f(x) =-2/- Type your answer without fractional or negative exponents. Use sqr...

A: Let's find. 

Q: general function M(x, y) or N(x, y) so that equation is exact.

A: We will find the function (general). 

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is pendicular to the ...

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Q: Recall from our lesson that a Non - Homogenous 2nd Order Differential Equation has 2 sides: The Char...

A: Given that, There are two differential equations following, (i). y'' - 3y' - 10y = 5e-2x (ii). y'' +...

Q: cion of the tangent line to the curve at the point

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

A: Given: limx→0+6x+1cotx   As we know from the limit rule; If the limit is limx→afxgx and it results o...

Q: The Center of Mass of a Thin Plate (region) Consider the region in the zy-plane bounded by the curve...

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Q: Let f(z) Find the values of a where f' (1) = 6. こ+7 Give exact answers (not decimal approximations)....

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Q: Directions: Use the circle below to solve for the missing values. 1. What is m CI? 2. What is m ∠I...

A: Given that:               NOTE: As per our answering guidelines, we can only answer 1 question or 3 ...

Q: 1. Consider the following vector, T = (-1,1), (a) Find two unit vectors parallel to v. (b) Find a ve...

A: Given,v=-i^+j^a) Find unit vector parallel to v.We know thatv^=vvv^=-i^+j^(-1)2+12v^=-i^+j^1+1v^=-i^...

Q: Find the nearest degree the directing angles of b = -i +3/2j+1/3k

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Q: 3(w-5) 2(w-2) 20. w+1 21. Solve for r: D=rt 22. Solve for W: P=2L+2W

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Q: Bottled Water Sales The following chart shows annual per capita sales of bottled water in the United...

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