Activity 1: Let's Compute! Directions: Investigate the discontinuity by using the three conditions. 1. f(x) 2 where c=-4 x+4 4x - 2 if x s 2 2. f (x) = where c=2 -2x + 5 if x > 2

Q: Question Find the absolute maximum and absolute minimum of the function f(x) = = - 2r² + 4 over the…

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Q: Find the solutions of the system of inequalities by graphing: ¤ + y 2

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Q: Let (2+2 ifz> 2 f(z) = { if-2<r<2 3-z ifz<-2 Which of the following is the graph of f? O None among…

A: Graph of given questions is given.

Q: A particle moves vertically (in inches) along the yoxis according to the position equation s(t)=> -…

A: We are given position equation of a particle moving vertically (in inches) along y-axis : s(t) =…

Q: In the differential equation (x + 2y - 1)dx + (2x + 4y - 3)dy = 0 , we let the substitution w =…

A: Substitute w=x+2y

Q: Written Works Evaluate the following Integrals. 1. S sin ycosy dy 2. sin3x dx 3 1 3. Jс S cos-y dy |…

A: Given: 1). I=∫sin3ycosydy  ....(1)   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1…

Q: 1 Show that f(x) =7(1+x) - 5/4 is a probability density function on [0, o); then find the indicated…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1…

A: The given equation of the curves are: y1=x2-3xy2=0 And the bounded region is as shown below: Now…

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y,…

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Q: The interesting relation is x^2+y^2 = 13. I have drawn it and completed part 1. Part 2 is determine.…

A: Topic:- geometry

Q: plve the following related rates and optimization problems. We want to build a greenhouse that has a…

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Q: Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether…

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Q: A sales representative for a company that produces electric can openers can sell x units of their…

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Q: Which of the following is false? 3 n The series. is divergent. 4+n n=1 1 The series - n=1 3+n4 is…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: man holds a rope that leads a horse. The horse walks in a circular path as shown by the dashed line,…

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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: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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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: If f (x) = Vx + 7 and g(x) find f(x) g(x). %3D Keypa Answer Keyboard Shorte f(x) · g(x) =

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Q: Determine whether the following series is convergent or divergente: (-1) " n7 +5 n= 1

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: Given problem:- Find the domain of the vector-valued function. (Enter your answer using interval…

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: From the given graph, the volume V is given by:V=2∫02π4-x22dx

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: Given equation passing through the points (5 , -3, -2)  and  -23 , 23 ,1

Q: Find the directional derivative of the function at P in the direction of f(x, y, z) = xy + yz + xz,…

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Q: 4. In the differential equation (6x–3y+2)dx-(2x- y-1)dy=0, we let the substitution dx=

A: Given differential equation, 6x-3y+2dx-2x-y-1dy=0              6x-3y+2dx=2x-y-1dy…

Q: s representation for f(x) 1+ x3 ° find the exact the power series obtained 2.

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Q: O (1, 5) О (-о, 1.5] O (-1, 4) О (-3, 2)

A: Let's find.

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: This question is based on application of definite integral and shell method.

Q: Find the gradient of the function at the given point. g(x, y) = 13xeY/x, (5,0) Vg(5, 0) =

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Q: (e) Compute y' if y2 = xe + ye-

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Q: (Show your solution) Compute the inverse of the function f defined by f(x) V+ 2. Determine the…

A: We have to calculate inverse of a function  And the domain and range of the inverse function.

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: A product is introduced to the market. The weekly profit in dollars of that product decays…

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: pien x = p sin p cos 0, y = p sin p sin 0, z = p cos p д(х, у, 2) a(p, 8, 4)

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Q: S sin x (1+ cos x) ecos *dx 2. S csc ³ () do 1.

A: 1) Given:       ∫sinx1+cosxecosx dx Integrate by parts:         ∫fg′=fg-∫f′g here  f=1+cosx→f'=-sinx…

Q: Find the arc length of the graph of r(t) = ev2ti + e¯v2tj+ 2tk, 0<t< v2 In 6 NOTE: Enter the exact…

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Q: Let f be a continuous function. Show that 2022 f(x) dx. 2022 dx

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Q: ꭍkg(x)dx=___ where k is a constant * a.(k/2)ꭍg(x)dx b. ꭍg(x) c. kꭍg(x)dx d.1

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Q: that has i +j and i – 18j as adjacent sides. NOTE: Enter the exact answers. ||d||= 19 ||d||=|17.12

A: Vector

Q: Compute f'(x) a.) f(x) = (x2+1)e-x^2 b.) f(x) = (4e-x-

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Q: 3. In the differential equation (2x+ ydx-3(2x + y+4)dy =0, we let the substitution dy :

A: We can solve the given differential equation  by  using  the substitution            u = 2x+y

Q: y" +y' + 1.25y = 0, y(0) = 3, y' (0) = 1.

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

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y+z=2…

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Q: Find the limit algebraically by factoring the expression first. lim X-6 -8x2-56x-48 x + 6

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Q: Knowing that harmonic series is divergent, which of the following series is also divergent by Limit…

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Q: 2. Locate the centroid (x, y)of the following areas: a) y3D Vx/2 + 2r/3 %3D I 2 ft

A: Given:    Centroid of the colored figure x,yWhere,x =MyM      &amp;       y =MxMMy = ∫02xfx-yxdx…