Given a rectangular box. Lengths are in cm 2x X X

Q: Find all relative maxima and minima of the following function. 1(x) = 4x³ - 3x² - 6x +17 f(x) has a…

A: Second derivative test for maxima and minima :  Consider the function f(x) Find critical point f'(x)…

Q: The electrical charge at the point (x, y) is given by C(x, y) = 4x² + 5y² - 8xy. If an object moves…

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Q: Find the distance between points P₁ (4,8,3) and P2 (10,14,6). A. 18 OB. 14 OC. 9 OD. 10

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Q: Express the vector as a product of its length and direction. 6i + 12j+ 12k 1 2 2 OA. 18 +3+3k OB. 18…

A: Given query is to express the vector as product of length and direction.

Q: I Given, dr=b(cos@dr+rsinºd€) ; r (ñ) =1, Find r(7). O 1 1+b 1+b 2 1 1+b b 1+b (1-b)

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Q: Find d dx d dx 2 8x² 3 8x² 3 7 2 5x² 7 2 5x =

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Q: Find the angle between u = - 9j and v=8i-3k in radians. Round to two decimal places. OA. 1.57 OB.…

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Q: Use integration by parts to evaluate the integral: 7z sin(z)dz

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Q: The graph of y = m(z) is given below. Answer each of the questions below the graph. 10+ 9 st…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

A: 1) Domain: The domain of a function is the set of input values for which the function is real and…

Q: 2. If r(t) = ti + cos(t)j + sin(t)k, evaluate (a) frit r(t) dt, (b) r' (t) (c) the parametric…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find all values x = a where the function is discontinuous. For each value of x, give the limit of…

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Q: Which of the following improper integrals are finite and well-defined? (Tick all that apply) (A)…

A: The answer is in step 2.

Q: Question 9 Let The third component of v=3 and w w xv= [2] - 1 2

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Q: Find c such that the function x ≤ c [x² - 8 10x 33 x>c f(x) = is continuous everywhere. C = с

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Q: Determine the graph of the equation. x² + y² +49z² = = 4

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Q: -1 dx 1 x 3

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Q: Find the solution to the Bernoulli equation. xdy = ( + 7 - x) dx ○ y³ = 1+ Cx-³ Oy³ = 1+ Cx³ ○…

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Q: using Part 1 of the Fundamental Theorem of Calculus. Enter the exact answer. Remember to include a…

A: We will find the required.

Q: dv Draw a dependency diagram, and write a chain rule formula for ds where v=h(p.q), p = f(s),…

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Q: 1) For what value(s) of a does m(x) = -4? Separate multiple answers with commas as needed. -1, 1…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph,  points are…

Q: If E is the solid described below with density function p(x, y, z) = x² + y2, find the following…

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Q: Find all values x= a where the function is discontinuous. For √x-9 k(x)=2e

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Q: Determine the x, y, and z components of the unit vector in the same direction as [5,-2,-6].…

A: NOTE: Refresh your page if you can't see any equations. . the given vector is  find the magnitude…

Q: Solve the initial value problem. d²y y = 2 dx = 4e x, y(0) = 2, y'(0) = 3

A: Here is the solution:

Q: The vector r(t) is the position vector of a particle at time t. Find the angle between the velocity…

A: To find the angle.

Q: 5. Given ƒ(x)= aeª+be¯* ; find f (0), f(x) + f(-x). a+b Show that f(2x) —ƒ (-2x) = [ƒ (x)]² − [ƒ (−…

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 5m (7x² - 6x) lim X→0 х

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Q: Use washers to find the volume formed by rotating the region enclosed by: 21.6 x 10 and y = 0 y =…

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Q: Evaluate the integral. 8y' dy 8 y 8y' dy 8 y - 4 - 4

A: Solving the problem by finding the value of the integration.

Q: Solve the following differential equation, give the general solution. 5ydx - x(y-4)dy = 0

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Q: Find the equation of the line tangent to the graph of f(x)=2x2−3x−3 at x=1.

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Q: 37. 6² ( So 1 1 t + 1 i+ 1 t² + 1 j+ t t² + 1 2 k dt

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Q: 3. Assume that f(x) is continuous on [a, b] and x1, x2,...,n are arbitrary numbers taken from [a,…

A: The given data is: Assume that f(x) is continuous function on a,b and x1,x2,........xn arbitrary…

Q: 1. Use the First Fundamental Theorem of Calculus to find the exact first quadrant area under…

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Q: Find the length of the following two-dimensional curve. /₁² =(1/2. (2t+1)3/2 3 r(t): for Ost≤8

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Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A: consider the given function f(x)=-2+x3 Find the first derivative of the function.  3x2…

Q: Solve the initial value problem. d²y dx² y = = 4ex, y(0) = 2, y'(0) = 3 ...

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Q: s dx = S-₁₂ ² =S= X 2 – ν -1-3v+v² dv

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Q: dz Find given: dt z = 3x³y, x= tº, y = −5+2t dz dt = 60t-151 -450t 60t-150 -150+60t In(180) x X…

A: Topic = Derivative

Q: Evaluate ftan tan4 r sec4 rdr +C

A: M=∫tan4xsec4xdx1+tan2x=sec2xd dx(tanx)=sec2x

Q: The equation y'-y=4te is a first order linear DE in standard form. True O False

A: The objective is to find the correct option .

Q: If z = xe², x = t³ and y = -3 + 5t then: dz dt

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Q: A record company has determined that the cost of producing CDs is $0.06 per CD plus $597.60 per…

A: to find out the profit function equation and also we need to find out the break even point.

Q: Select any necessary conditions for a function to be differentiable over its domain.   Question…

A: We know that a smooth function is a function that has continuous derivatives up to some desired…

Q: Find the Taylor series generated by fat x = a. f(x) = 7Xia=1 Choose the correct answer below. Ο Α. 7…

A: To find the Taylor series generated by f at x=a. fx=7x, a=1

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: You know that: • 9(1) dt = 25 . . g(3) = 3 √3 g(9) = 3 Evaluate: To 3 g'(x) 9+ (g(x))² da [

A: Given:  ∫39gt dt=25g3=33g9=3 To Find:  To evaluate ∫39g'x9+gx2 dx.

Q: Determine the points at which the function f to the right has discontinuities. For each point state…

A: Condition of continuity1. fa is defined2. limx→afx exists3. limx→afx=fa

Q: Use the four-step process to find f'(x) and then find f'(3), f'(4), and f'(8). f(x) = 2x² − 9x + 10…

A: To find f'(x)