Find Duf at P. 1 f(x, y) = 3(1 + xy) ³/²; P(5,3); u= NOTE: Enter the exact answer. Duf = i+ 1

Q: the family of solution of the equation (x-2y)dx+(2x+y)dy=0.

A: We will find the required.

Q: Find the linear approximation L(x) of the function ¹ƒ(x) = x² + 2x³ at a = -1.

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Q: Find the horizontal asymptote, if any, of the graph of the rational function. 18x 8x² +9 f(x)=…

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Q: Given g1x2 = 2x2 - 4 + 7, find x so that g1x2 = 10.

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Q: Find Vz. 5xeby x + 6y NOTE: Give your answer in unit vector notation; that is, in terms of i and j.…

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Q: 2. Find the equation of the tangent line to the graph of f(x) = x³ - 2x² + 5x -3 at the point (1,1).

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: True or False The cube function is odd and is increasing onthe interval 1 - q, q 2.

A: Given, fx=x3

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Q: Consider the space curve (t) = (6 cos(5t), 8 cos(5t), 10 sin(5t)). a. Find the arc length function…

A: As per our guide line if multiple questions are posted we are supposed to answer only the first one.…

Q: Differentiate the square root of x / (1+x

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

Q: Find the horizontal asymptote, if any, of the graph of the rational function. 16x 2 8x²² +3 f(x) =…

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Q: Differential equations -Separable dy/dt=3+5y

A: We can solve the differential equation in the below steps.

Q: How many 3-letter words can be made from the letters WASTEFUL if repetition of letters is allowed?…

A: Topic- Permutation and combinations We are given a word WASTEFUL.

Q: Rewrite the following expression in terms of exponentials and simplify. ln(cosh(8r)…

A: we know that coshx =ex+e-x2sinhx=ex-e-x2nowcosh2x-sinh2x=ex+e-x22-ex-e-x2…

Q: (ƒ-¹ of ¹)(-2) 78. (g-¹g-¹)(8)

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Q: Two sides of a triangle are 2 m and 8 m in length and the angle between them is increasing at a rate…

A: Given query is to find the rate of change of area.

Q: sketch the graph of each function. Be sure to label three points on the graph.   f1x2 = 3

A: Concept Used: Graphing Substituting values to x and y  in the functionfx , the intercept points can…

Q: Find the Derivative of f(x)=128x/(x^2+64)^2

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Q: მე Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2√√2, 4 ) 80 1 where…

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Q: Use cylindrical shells to find the volume of the solid formed by rotating the region bounded by y =…

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Q: A street light is mounted at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the…

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Q: In the following exercises, evaluate the triple integral f(x, y, z)dV over the solid B. B = {(x, y,…

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Q: f(x)= 3x³(2x-1)¹

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Q: unction. (Enter your erivative. (Enter you

A: We have to find the following conditions according to the given information

Q: Find the marginal -revenue function if the demand function is p=(15)/(ln(q+4)).

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Q: A computer password is required to be 8 characters long. How many passwords are possible if the…

A: Solution: A computer password is required to be  8 characters long. The password is in the form :  1…

Q: Find the equation of the curve, if at any point on the curve y'' = 4x - sin 2x and that (π/2, 0) is…

A: Topic:- algebra and application of integration

Q: The voltage, V (in volts), across a circuit is given by Ohm's law: V = IR, where I is the current…

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Q: For the function f1x2 = x2 , compute the average rate of change: (a) From 0 to 1(b) From 0 to 0.5(c)…

A: given function isf(x)=x2

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x² -…

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Q: Find the area of the triangle with vertices P(1,5, –4), Q(0, 0, 0) ar R(3, 4, 1). NOTE: Enter the…

A: We have to find the area of triangle .

Q: Find the periodic withdrawals PMT for the given annuity account. (Assume end-of-period withdrawals…

A: Solve by formula

Q: For the function graphed below, find the values of x at which the derivative does not exist. (Enter…

A: Given the graph of a function  f(x) . By using graph we need to find points where f(x) is not…

Q: Topic: Vectors and Geometry of Space → identify and sketch the following item. identify its traces…

A: The general equation of the elliptic cone is given by z2=x2a2+y2b2   The general equation of a…

Q: 4. Find the derivative of the function. f(x) = In(tan x) 5. Find the derivative of the function.…

A: I am attaching image so that you understand each and every step.

Q: Let r(t) = (2t5 + 4, − 5e-4t - 3 sin( – 5t)). - " 1 fr(t)dt (don't include the +C) Find fr(t)dt = (…

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Q: Use the Chain Rule to calculate the partial derivatives g(x, y) = sin(x² + y²), x=3v- 3u, y = 4u +…

A: By using chain rule to calculate the partial derivatives ∂g∂u, and ∂g∂v.gx, y=sinx2+y2, x=3v-3u,…

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Q: Use transformations of the standard cubic function, f(x) = x³, to graph the function h(x) = 2x⁰. UL

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Q: Evaluate √√cos cos x sin³ x dx.

A: ∫cosxsin3xdx

Q: Divide using long division. State the quotient, q(x), and the remainder, r(x). 4x³-5x²+6x+7 4x² + 3x…

A: Given, 4x3-5x2+6x+74x2+3x+4

Q: Find the curvature of the curve r(t) = (1 + t, 2 − 4t, 4 — 2t) at the point t = = 0.

A: To find curvature of the given curve

Q: write the function whose graph is the graph of y = x3, but     Reflected about the x-axis

A: Given, y=x3

Q: Evaluate the integral 9x³ (x + 1)³ Note: Use an upper-case "C" for the constant of integration. ✓ dx

A: We can evaluate the given integral by using the following formulas.

Q: Find 7'' (t), given 7'(t) = (te²t, − cos(5t + 5), 3t ln( − t)). ř'(t) = x, 4 cos(2t) = -6e-2t x,…

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Q: Evaluate 6.² sin (3x) cos(5x) dx.

A: As we know the trigonometric identity; sinacosb=12sina+b+sina-b And the common integral is:…