Find the length of the polar curve r = 0², 0≤0 2T.

Q: Write the following as a single logarithm. Assume all variables are positive. 7 log (y) + 3 log; (c)…

A: Given data 7 log3(y) +3 log3(c)

Q: Find the equation of the ellipse satisfying the given conditions. Write the answer both in standard…

A: Foci =( 0, +-1) Vertices= (0,+-3)

Q: 13) fx³ In(x) dx

A:

Q: Solve the initial value problem. dy y dx x X 5|8 = 5xe*, y(1)=5e+7 The solution is y(x) = -

A: The given differential equation is;  dy/dx - y/x = 5xex, y(1)=5e+7

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A: ∫24(9-x2)dx,    n=4

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A:

Q: Solve (D2+20D+200)y = 10 O y = e-10x (c₁sin10x + c₂cos10x) + 20 Oy=e-10x (c1sin10x + c₂cos10x) +…

A: Given

Q: Find the second derivative of the function. 1x)-(3x²³ +7) Op 63x (7 + 3x) 5 (14+63x³) = f" - 63x (7+…

A: given function is f(x)=(3x3+7)7

Q: Which of the following best describes the derivative of the function at a point?

A: The derivative of a function in calculus of variable standards the sensitivity to change the output…

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A:

Q: The salinity of ocean water changes depending on how deep you are in the water when you measure it.…

A: From the given table

Q: #6 #8 ∞ Σε n=1 ∞ Σε arctann n' +1 2 100⁰ n! Hint: Integral Test is conv Hint: Ratio Test is…

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Q: Solve the following IVP: f'(x) = 4x - 1 given f(2)= 5

A: Given: f'(x)=4x-1, f(2)=5 We are required to: Solve the given differential equation.

Q: find dy/dx by implicit differentiation. tan(4x+y)=4x. Use the original equation to simplify your…

A:

Q: Find the equation of a line tangent to the curve ²+²=9 at the point (2, √5). In addition, find the…

A: To find out the equation of the tangent line to the given curve at the point and also need to find…

Q: 14) [2.30" dr et -dx 3+e*

A:

Q: Sketch the set of points in the plane which satisfy the equation y + 2 = 3(x − 4)

A: We have to draw the graph for y+2=3(x-4)

Q: find the center, vertices, foci, and asymptotes of the hyperbola. 9x² - 4y² = 36

A: 9x2-4y2=36

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: Given that a=2,3 , b=3,-1

Q: Given the graph of y = g(x), estimate the value of g'(2). (a) -4 (b) -1 (c) 0 (d) 1 $10 3 (c) 4

A:

Q: Q2 Given marginal cost is C'(x) = 2x + 5. Find the cost of the 3rd unit.

A:

Q: use the given information to determine the equation of the parabola. Focus: (3,6), vertex: (3,2)

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Q: 2. Suppose an object moves along a line with velocity v(t) (measured in m/s), for t≥ 0, as shown…

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Q: a

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Q: Given the demand function D(p) = 325 Р

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Q: 6) 1) (2x²-3x+2)dx -5

A: Given that integral is

Q: 1 Find the probability that a randomly selected value of X lies in the interval [4, 6] if f(x) = 63…

A: Probability density function : f(x) = x263 To find: the probability that a randomly selected value…

Q: find a power series representation (your power series representation x=0) f(x)=2/(1-x^2) for the…

A: We need to find a power series representation for the function. (the power series representation…

Q: 7. Find the derivative of the following functions: a. y = esinx b. y = (5x6x8)14

A: (a) given y=esinx

Q: Find an equation of the plane. The plane through the point (8, 9, 3) and with normal vector 5i + j -…

A:

Q: (D2 – 2D + 1) y = xe + ** e X 2

A: The given differential equation is;  (D2-2D+1)y=xe+ex/x2

Q: An orchard finds that if they plant 95 trees per acre, each tree will yield 40 bushels of fruit.…

A:

Q: Evaluate the following integral in spherical coordinates. The integral calculates the volume of the…

A: To evaluate the following integral in spherical coordinates. ∫0π∫0π6∫4 sec φ9ρ2 sin φ dρ dφ dθ

Q: How much money must be invested now at 10% interest compounded continuously so that $120,000 will be…

A:

Q: The angle of elevation of a flying kite is 77°11′53″ . If the other end of the 198 -foot long string…

A: Given: The angle of elevation of a flying kite is 77°11′53″. The other end of the 198 foot long…

Q: Find [[ (3x + 4y)dA (3x + 4y)dA where R is the parallelogram R with vertices (0,0), (1,-2), (5,4),…

A: The Jacobian determinant must be calculated and the change of variables must be applied in order to…

Q: Solve the given initial value problem. y'"'-8y" +27y' - 44y=0; y(0)=1, y'(0) = 0, y''(0)=0 y(t) =

A: The differential equation is y'''-8y''+27y'-44y=0 having initial condition y(0)=1 , y'(0)=0 and…

Q: Subject: calculus

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Q: Express the equation in exponential form. 4y + 3 = ln (2x + 2)

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Q: Given the demand function D(p) = √250 - 4p, Find the Elasticity of Demand at a price of $13 At this…

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Q: Find the general solution to a second-order homogeneous linear differential equation for y (x) with…

A: One solution e2xsin2x.

Q: 5. If f(x) = 2x² e*, find ƒ '(1).

A: Explanation of the answer is as follows

Q: Function with given infinite power series. x20 - 2 - + 5 28 x² 7 +

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Q: 18. lim 2+3 √3x + 16-5 x - 3

A:

Q: Determine the point (x, y) on the unit circle associated with the following real number s. Write the…

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Growth of Bacteria Under a set of controlled laboratory conditions, the size of the population of a…

A: give bacteria growth function f(t)=3t2+2t+1

Q: 4 4 56. xy + xy = 1

A: Given equation xy4 + x4y = 1 Formula used ddx( u.v ) = udvdx + vdudx

Q: Once an airplane has reached its cruising altitude, its computer shows the destination to be 2,400…

A: The linear function we used to model the distance of the plane from its destination is an example of…

Q: 2. Describe a series of transformations that would transform f(x) = |x| +5 into g(x)=2x-1 Be sure to…

A: Describe a series of transformations that would transform f(x)= |x| +5 into g(x)= -2|x| -1 .