Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = Vx - 3 and whose nomal line is parallel to the line 6x + 3y – 4 = 0. Sketch the graph.

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that…

A: answer is in next step

Q: determine the relation x^2 + y^2 = 13. dy/dx in terms of x and y using implicit differentiation.

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Q: Oil from a leaking oil tanker radiates outward in the form of a circular film on the surface of the…

A: We have to find the rate of change of radius when the area is 1225π sq.mm

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = | t*dt…

A: By using Part I of the Fundamental Theorem of Calculus:f'(x)=x4

Q: 2r Find the absolute maximum and absolute minimum of the function f(x) = 2x 3 over the interval [0,…

A: Absolute Maximum and Absolute Minimum in a closed interval: step 1 : Find the critical point of the…

Q: Solve the system by using the inverse of the coefficient matrix. X+y+z =1 3x + 4y – z =1 2x - y-z =3…

A: Let A be the coefficient matrix of the system.So,A=11134-12-1-1AX=BX=A-1Bwhere X=xyz, B=113

Q: A box with a square base and open top must have a volume of 186624 cm³. We wish to find the…

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Q: fx) dx = -5x* + 3x² + 6x + C

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Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: 00 Let f(t) be a function on [0, 0). The Laplace transform of f is the function F defined by the…

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Q: Solve the following differential equation:   y′′+9y=0; y=3,y′=3 at x=π/3

A: Given y''+9y=0; y=0, y'=3 at x=π3 To find the Solution:

Q: Solve the system of equations by substitution. fx + y = -9 x- y = 13 Ox = 9, y = -11; (9, -11) Ox =…

A: Explanation of the answer is as follows

Q: Find the length of the curve defined by y = 3 ln from x = 8 to x = 9.

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Q: y2 = 20x О А. (5,0), х - -5, у-аxis В. (5,5), х%3D5, х-аxis С. (5,0), х%3D — 5, х-аxis D. (0,5), y…

A: Given query is to find the the focus , directrix and symmetry for the parabola.

Q: Suppose that P = (x, y) has polar coordinates (r, = ). Find the polar coordinates for the following…

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Q: dx Evaluate: xV x2 + 4 x² + 4 – 4 + C x2 + 4 + 4 - A) 4 x² + 4 – 2 +C x² + 4 +2 Vx² +4-2 + C Vx² + 4…

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Q: Txーt e lim 4x² 4,2 +4x

A: Consider the limit  limx→0 e2x-14x2+4x

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: Question The statement below is of the form f(x) dx = F(x) + C. Find f(x). rco) dx = 2x* + 3x* + 4x…

A: Use derivative for finding the value of f(x)

Q: 2hx + h“ 4. Find lim h→0 h А. 2х В. 2х +h С. 2 + h D. 2h 5. If f(x) = 2x – 1, what is f(x + h) –…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: This dota shows fthe amount of sugar (in pounds) in different packoges How much total sugar is…

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Q: The following students U= {Hepburn, Dames, Cooper, Rolle, Hanna, Smith, Bain} were classified in the…

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Q: Lal 3+4" 2" which of the following is correct? To use the comparison test on the series O None of…

A: Given query is to find the correct option option.

Q: If f(x) = kx, determine the value of k that makes f(x) a probability density function on 0<xs4.

A: Given,           fx=kx2To find : Determine tha value of k that makes fx a probability density…

Q: Find the eccentricity, the type of conic, the directrix, and sketch a graph: r = (3) / (1 -…

A: Let's find.

Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation"…

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Q: raph the following horizontal parabola, and give the domain and range. Ay 10 x- 4 = - 2(y - 3)2…

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Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

A: The given logarithmic expression is  log5x3y2z

Q: Evaluate the integral sin(t)dt

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Q: Question Evaluate the following limit using L'Hospital's rule. lim X09e - 9 18x] Provide an exact…

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Q: x2 a) lim X o e2x

A: We have to find out limit of given function using  L' Hopital's Rule which is as follows in step 2 .…

Q: 4. An object is moving along a horizontal line according to the position function s(t) = 2t - 21t? +…

A: Let's find.

Q: At a dinner party hosted by The University: • 13 guests had steak and chicken • 29 guests had steak…

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Q: how do i solve this calculus question ?

A: In the given problem we have to find out that whether sequences are monotonic are not .

Q: x 6. Copy each graph of (x) and g(x). Then, apply the superposition principle to graph f(x) + g(x).…

A: Graph of the functions f(x) and g(x) are given, we have to graph f(x)+g(x)

Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: 6. Set up the integral to calculate the area between the curves fG)= g(x) =-r+2 [ (fy)-g(y)) dy А.…

A: The region is bounded by,f(y)=y2 , g(y)=-y2+2 and y=-1

Q: ; Suppose v · w = 8 and ||3 x w|| = 2, and the angle between v and w is 0. Find (a) tan 0 (b) 0 =

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Q: Find the area of the region enclosed by the rose r = 18 cos 30. NOTE: Enter the exact answer.

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Q: Use a graphing calculator to solve the nonlinear system. y = log (x+ 5) y =x? Select the correct…

A: this question has been solved using a graphing calculator desmos.

Q: Find the area of the region bounded by the graphs of the given equations. y%3 5x- x, y = - 2x The…

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

Q: Question dx If z? = x +y. dt dy = -3, and z > 0, find dt dz -2, at (x, y) = (4, 0). dt %3D %3D…

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Q: 5. (4xy-y²+10x²+sin x)dx+(2x²-2xy+ cos y )dy=0

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Q: Find the equation of the tangent line (assuming it exists) to f(x) = x² + x at x = -2. Give your…

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Q: Find the values of a, b, c, and d in the matrix equation below. [:] 10 -5 -8 -1 b. + 2 -8 -10 7 a =…

A: We will find the value of a,b,c and d of the given matrix in the following step.

Q: Consider the following lines: 4:z=1,y-1=-4,2=1-3t :z=2s+1,y=1-3s,z=1 y+1 z-1 2a Find the…

A: Explanation of the answer is as follows

Q: 4. (2x2-у?)dx+2хydy-0

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Q: x <0 2r3 + 3r2 – 12x, x 0 10xe", f(r) = a. Find all the critical numbers of f. b. Find the extreme…

A: a)  For x&lt;0    Consider f'(x)=0  ⇒10(ex+xex)=0  ⇒10ex(1+x)=0  ⇒1+x=0  ⇒x=-1For x≥0Consider…

Q: :-1 and g(x) = "- Vx +1 Let f(x)= arccos 2arctanx. (a) Find f'(x) and g'(x). V-1 *-2 arctan Vx ?…

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