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Q: 12. f (x) = xe -x

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Q: given

A: Please refer to the image below

Q: funchoN f whose second derivative is f ")= 5x+2sin(x If fo 3 and fro)= 3. what is fe?

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Q: Directions: In implicit differentiation, we differentiate each side of an equation with wo variables…

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Q: Given vectors a = (1,2),5= 2,-1), find 4a-35. (-2,-11) (2,-11) (-2,11) (2,11)

A: Given vectors are:- Vector a =<1,2> vector b =<2,-1> Find :- 4a-3b

Q: How do you take the integral of 2 * sqrt(t^2 + 1) ?

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Q: For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is…

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Q: Consider the following. x = 9 sin?(t), y = 9 cos?(t) (a) Eliminate the parameter to find a Cartesian…

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Q: ) Find the y’’ (second derivative) of the following in its simplified form. Do not skip the steps…

A: This is a problem of differentiation of the function. Based on the general formula we will solve the…

Q: Given the following vectors, add the vectors and find the magnitude and angle of the resultant…

A: 4. Given, v=(5,9) u=(-5,-9) According to given, Resultant(R)=((5-5)²+(9-9)²)1/2 R=0 Angle is given…

Q: A stone is thrown straight up from the edge of a roof, 600 feet above the ground, at a speed of 16…

A: The answer is in below steps.

Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: 1. Integrating Factors Found by Inspection: y(x + y'exy)dx + x(y'exy - x)dy + = 0 when y(0)

A: y(x+y3 exy)dx + x(y3exy-x)dy=0xy dx -x2 dy +y3[x exydy+yexydx]=0xy3ydx-xdy+[x exydy+yexydx] =0xyy dx…

Q: #2. Find the slope of the tangent line to the curve at the indicated point: (a) x² +x°y² – y° =13 at…

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Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLI 3x 1. Y= Arctan

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: dy dx 1+8sin ?x 1 Given tan(3y)=3 tan x . Show clearly that

A: As we know that; The chain rule: fgx'=f'gx·g'x   The trigonometric identities; 1). tanx=sinxcosx 2).…

Q: Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the…

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Q: Find the Cartesian equation of the polar equation p² = 2[1+ r(cos 0 – sin 0)] and identify its…

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Q: Sales of a Product The total number of units of a new product sold t months after its introduction…

A: see below the answer and explanation

Q: For 6. the region bounded by the given curves is rotated about the specified axis. Sketch the region…

A: Given

Q: Given vectors a = (-1,-2),5= (-2,3), c= (3,-1),đ = (-3,2) find the dot product of 5 and d. -12 -1 12…

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Q: 38. f («) — е -3a; c= 2

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Q: #4A

A: answer is in next step

Q: 20t y = (x-2)2+40 ABOUT THE X-axis -2 0 2

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Q: A function f is defined by f(x)=x' – 3x² – 24x , where xeR. (i) Find the coordinates of the…

A: Given that fx=x3-3x2-24xi  stationary points occurs…

Q: Find the domain and range

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Given

Q: 1„2 The graph shown is f (x) = ±x². 4 3 21 1 54 3-2 -14 1 2 3 4 5 -2 3 4 If g(x) = `f(t) dt, what is…

A: This is a problem of antiderivative function. Based on the general formula we will answer the…

Q: За. й —; й —

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 6)Let f ( x ) = x4 + x3 - 3x2 + 1 a)Find all the hypercritical values. b)Determine the intervals…

A: The given function is f(x) = x4+x3-3x2+1 ............................ (1) We have to a)Find all the…

Q: f(x) dx = -4, f(x) dx = 6, g(x) dx = 8 - If g(x) dx b. c. 3f(x) dx d. dx x) - g(x)] dx g(x)] dx e.…

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Q: 3X-1 xp +4

A: Follow the procedure given below.

Q: 25x² -9 3. dx

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Q: e*(y' – y) = 2xy?

A: Given

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an…

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Q: 2. A= B = 23 DA+B @ Ao+B

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A: The vector v has,magnitude, v=2angle, θ=0°

Q: coordinates

A: We have to choose the correct option according to the given information

Q: 9y²dy 1+ y*

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Q: Use THIS standard form for a tangent plane: - fz (x1, yı) * (x – x1) – fy (x1, yı) * (y – y1) + (z –…

A: Given

Q: 2, 22, 23 5 67 8 * 3. Test the series

A: Write the series as summation and use ratio test .

Q: 5) The solution of the volume of triple integrals r1-x 5-r dz dy dx is:- 30 A) 5 20 В) з С) 30

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Q: Find the derivative using the definition 2х-3 y = 3x-2 What is the solution if the answer is: 2х-3…

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Q: dx 4. 3 3 х3Vx2—9

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Q: Derive the derivative function for secx and express your answer in product form.

A: ddx(secx)=ddx(1cosx)ddx(secx)=cos(x)ddx(1)-1ddx(cos(x))cos(x)2ddx(secx)=cos(x)0-1-sinxcos(x)2ddx(sec…

Q: Dver what interval is the graph of the rational function positive but decreasing? 4. 2 -4 -2 -4 a)…

A: Topic:- calculus

Q: mt) cos(r b) f(x) = /2r(4°

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Q: 2. The function g(x) is defined for -3Sx5 3. The behaviour of g'(x) and g"(x) is given below.…

A: A)-3<x<-2, g'(x)<0and-2<x<1, g'(x)>0Function decreases over (-3, -2) andincreases…

Q: (i) y= 3e –e**2 +2 sin (x² +1)

A: