Find the equation of the plane passing through the points O=(0,0,0), A=(−4,5,1)and B=(−1,0,−6)

Q: Consider f(x)=5x-3-41/x^2 Find the average rate of change of f(x) with respect to x over the…

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Q: The curvature of a plane parametric curve x = f(t), y = g(t) is given by |x y - yx| [x² + y2]3/2…

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Q: Solve for y' if y = sec55x - tan²5x A. 0 B. 1 If y = x[sin-¹ (sin x)], find y' A. 2x B. -2x C. 5…

A: (1) Given that , y=sec55x-tan25x y'=?

Q: The root of e^x -2 is known to exist in (0,2). Find an approximate value of the root within a…

A: Given: fx = ex-2 The root exist  from 0,2. ------------------------------Aim: To find the root with…

Q: Use the given graph of f to find a number & such that if 0 < x - 3| < & then. If(x) - 2| < 0.5. y 8…

A: Given graph:-

Q: Find div F if F(x, y, z) = (x2 + y) i + z2 j + (ey - z) k.           A . 2xy i + k          B. 2x…

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Q: Find the relative extreme points of the function, if they exist. Then sketch a graph of the…

A: The given function is  f(x)= x3-12x+7  We have to find  a) relative minimum points b) relative…

Q: Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: If y = √4x²+2sin-¹ A. 2-x 2+x A. 0 B. 2+x 2-x ,then y' equals, C. . Find d if y = arcsin√2x +…

A: Topic- Derivative of a function we are given y=4-x2+2sin-1x2and y=arcsin2x+arccos2xwe know…

Q: Rewrite each of the following as a power function in the form kx", or state that it is not a power…

A: Given, 5x3;x3;72x

Q: Sketch the region bounded by the paraboloids z = x² + y² and z= 32-x² - y².

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Q: Find the domain of the following function. Give your answer in interval notation. Provide your…

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

Q: Consider f(x)=5x-3-41/x^2 c) Find the equatino of the tangent line at x = 2 to the graph of y =…

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Q: Use the Power Rule to compute the derivative. (Use symbolic notation and fractions where needed.) d…

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Q: - IV. Solve the VSDE (x² − 3)dx + xydy = 0.

A: Topic = Differential equation

Q: Decide which of the following are true. Choose all that apply. Review intersections and unions here.…

A: Operations on Sets   Union of Sets If set A and set B are two sets, then A union B is the set that…

Q: Use a grapher to find all local maxima and minima and the values of x where they occur. Give values…

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Q: What is the average velocity of the curve y= square root of ( x2-2x) over the interval of [ 2,7]

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Q: EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²- 8x +9 at the point (2, -3).…

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Q: The root of e^x-2 is known to exist in (0,2). Find an approximate value of the root within a…

A: The given function is fx=ex-2 which has a root in the interval 0,  2.

Q: Given f(x, y, z) = x²y³z − 3xy²z³ + 5x²z − y³z, find fxyz

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: The given integral is sqrt(5+1/x)/x2.

Q: EXAMPLES Find an equation of the tangent line to the parabola y--&x+9 at the point (2.-3). SOLUTION…

A: Find equation of tangent line

Q: Find the particular solution of the following equation by first finding its general solution: y''…

A: Given, y'' - 4y = 10

Q: 5. Show the equation sin² x + 2x = 3 3 has exactly one solution. has exactly

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Q: The unit tangent vector for the parametrized curver (t) = (8, cos 2t, 2 sin 2t) at 0 < t < 2n is

A: To find the unit tangent vector

Q: Match the equation with its graph. x² + 2z² = 1 X* x.

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Q: Given and f'(-1) = 4 and f(-1) = -6. Find f'(x) and find f(2) = = f"(x) = = 2x + 3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Calculate the value of the derivative of the function:  y = cos (sin x) at the point x = 3π/2 to 2…

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Q: U Substitution (a) State the Substitution Rule. Explain its connection to the Chain Rul- (b)…

A: Topic = Integration

Q: The range of y = tan-¹ x is A. R Evaluate lim h-0 A. undefined B. [-1,1] (x-h)³-x³ h B. 3x² C. x +…

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Q: 7- 7+3 7-2 + 3 北

A: Solution ) ( y + 3 )/( y - 2 ) + ( y - 3 )/( y + 1 )  L.C.M. of ( y - 2 ) ( y + 1) = ( y - 2 ) ( y +…

Q: Differentiate implicitly to find dy/dx. Then find the slope of the curve at the given point. x²y² =…

A: Given expression: x2y2=49                ............(1)

Q: If a force of 49 N stretches a spring 0.7 m beyond its natural length, how much work does it take to…

A: We have given  Force = 49 N Using Hook's law F=kx ........(i) k=Fx Put F=49 N and x = 0.7 m k=490.7…

Q: i) S 3+6x+4x² −2x³ (x4+3x²) ·dx

A: The given integral is (3+6x+4x2-2x3)/(x4+3x2).

Q: Write the standard form of the equation of the circle with the given center and radius. Center…

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Q: Hi. It's kind of hard to understand the transcript. Do you have a handwritten solution? Thanks

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Q: 1. Three vectors in space are given as = 3x + 2y + 42 K L = 2x − 3y + 2 - M = -x-4ŷ in cartesian…

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Q: A car wash firm calculates that its daily production (in number of cars washed) depends on the…

A: The question is different . Here , differentiate w.r.t to n

Q: Qe Evaluate the following integrals, then reverse the integration order ( a) y dx dy.

A: Consider: ∫02∫04-y2y dx dy=∫02y x04-y2 dy=∫02y 4-y2-0dy=∫024y-y3dy=2y2-y4402=222-244-202-044=8-4=4…

Q: Eliminate the arbitrary constant for y=5+Ae^-x

A: Given function, y=5+Ae-x That is (y-5)=Ae-x                                  (1)

Q: Use the tabular method and the properties of limit to find the limit lim x→1 2x + 2-x 3

A: Since we have to find limit at x=1 by tabular method then we start the table from 2 to 1 and from 0…

Q: Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a…

A: we need to find out thr dimensions that will minimize the surface area

Q: Determine whether the given DE is exact or not. Do not solve the differential equation. 1. (3x²…

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Q: Check the exactness and obtain the general solution y'=x^3 - 2xy

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Q: Determine the solution xy³ dx + ye of the 1st Ordered Differential Equatio *dy = e*dy

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Q: Differentiate the following function. f(x) = x5 e5x f'(x) =

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Q: Minimize the function M = 3x² + 3y² subject to 2x + y = 16 and find the values of x and y at which M…

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Q: f(x,y)=(5x³-4y³)exp(3x)+ 4xy

A: To be called homogeneous function f(x,y) must satisfy the below equation .                f(λx ,λy )…

Q: 5 Spending on travel and tourism (in billions of dollars) for the years 1991-2009 is given in the…

A: Concept: Power function: A function having a single term that is the sum of a real number, a…