IV. Exercises A. Solve the following integrals: (1) /20. (2) / (2e + 4"). da (3) 2(5") dr

Q: 3.) 124-1|dx Evalnate: dt given taat Ina = 9 Evalmate t

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A: We need to determine length of RA.

Q: Evaluate the integral [[(ate?) i+ (o-8) j+ (3) k]at 0. S[(t022) i+ (e-) j+ (3)kJat = i+ ()j+ ( )k (T...

A: The integral,      ∫014te2t2i+e-3tj+3kdt

Q: 77. The rate at which water leaks from a tank, in gallons per hour, is modeled by R, a differentiabl...

A: Consider a function y = f(x) .Then f '( x0) is the rate of change of y with respect to x at the poin...

Q: Use the Laws of Logarithms to expand the expression. 5 log2 9t2

A: Apply log rule:  logaxy=logax - logay

Q: Solve the initial-value problem by using integrating factors. y' = y + 8xex, y(0) = 8 y(x) =

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Q: Find the exact arc length of the curve y = 3x3/2 − 1 over the ineterval [0, 1]

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Q: The point P has coordinates (-1, 4, 11) and the line / has equation r = (i) Find the perpendicular d...

A: The perpendicular distance, ?,between a point ?(?,?,?) and a line with direction vector d→ is given ...

Q: This exercise uses the population growth model. A certain culture of the bacterium Rhodobacter spha...

A: A)n(t)=n0 2taAt t=0,n(0)=1515=n0 20n0 = 15The bacteria doubles every four hours;At t=4 hours, 2(15) ...

Q: . Sketch the graph h(x) = x2 -x-12. Then, a.) Determine the line tangent to h(x) at x=c. What is it...

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Q: Find the general solution of the system y' = Ay where A = 1 2 -1 4 y(t) = c1e' + c2et y(t) = c1e2t 2...

A: Here, the given system is: y'=Ay where A=12-14

Q: Given the triangle below, find csc(0). Enter an exact answer in fraction form. 3 4 5

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is ...

Q: Which of the following is the solution to the differential equation with the initial condition y (3)...

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Q: Simplify the trigonometric expression. cosx(secx cosx) |

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Q: 12 + csc 0[sin 0 + csc 0]d0

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Q: +00 2 -1)"+1(3n)! 3n+1

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Q: Shaw Abooraically that Fand 6 ace.ivee F)=-3x2+5,X20 gW=D5-x 3. theN explain why a restriction was p...

A: if we have to find inverse of function then interchange the x to y and we get f-1x.if y=fxx→yx=fyy=f...

Q: Differentiate f(x) = arcsin(3x). Use exact values. %3D f'(x) =

A: Solution is written in below steps.

Q: 00 (-1)+12" n² +3 Determine the interval of convergence of

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Q: Determine whether the improper integral diverges or converges. 00 dx 12 converges O diverges Evaluat...

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Q: Integral from 0 to 1 of (3^x)/(e^x). The answer should be decimal

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Q: he directional de -) = 3x?y -4xy 3x², 2. %3D ne giu divection gie

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Q: Watch help video Given the function f (x) = x + 6x² + 12x absolute minimum value of f on the closed ...

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Q: Give the equation of the horizontal asymptote, if any, of the function. g(x) x2 + 8x - 3 x- 3 Oy=0 O...

A: Since, when the degree of numerator is greater than degree of denominator by one then there is no ho...

Q: If (an)? – (an-1)(an+1) = (-2)" for n>1 and ao = a1= 1 then az = a ) 0 b) 5 c)-3 d) 1 e) none a b. o...

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Q: 5+x-1 dx x3+1 4.

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Q: Find constants a and b so that the minimum for the parabola f(x) = x- + ax + bis at the point (5, 9)...

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Q: 6. Let a be a real number.

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Q: Find a solution for y in terms of x that both satisfies the differential equation and passes through...

A: We have to find the solution of differenrial equation

Q: The position of a car traveling along a highway is given by the function s(t) = 21* - 61-612 + 3 whe...

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Q: 25 Given the function f(x) = x°+ x° + x*, find all x-values where f has an inflection point.

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Q: Letting I répresent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up...

A: Rate of change of salt concentration = difference of inflow salt concentration and outflow salt conc...

Q: OFind the linearization L (1, y) of the function f (z, y) = /176 – 4,' - 16y at %3D L (z, y) = Note:...

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Q: Question The position of a hummingbird flying along a straight line is given by the function s(t) = ...

A: Here, to find the interval when the hummingbird speeding up.  

Q: The angle between the vectors = (6, -2, 3) and 7= (1, p, -2) is cos Determine the value of p.

A: Given:  The angle between the vectors a→=6, -2, 3 and b→=1, p, -2 is cos-1-114. To Find:  To determi...

Q: Selected values of f(x) are shown in the table below. What is the e10 trapezoidal sum approximation ...

A: We have to find ∫410f(x)dx  

Q: Use the sum and difference identities to simplify the expression. sin(-75)

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Q: 25 1. If cscy = 24 %3D

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Q: PERFORMANCE TASK Carl and his friend James are having trouble using the different methods for findin...

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Q: 3 A bicycle wheel rotates 400 times per minute. If the rider removes his feet from the pedals, the w...

A: The objective is to find how many times the wheel will rotate in the eighth minute.

Q: SHOW YOUR SOLUTIONS. I. Eliminate the arbitrary constants. 5. (x – a)² + y² = a²

A: Given :   (x-a)2+y2=a2

Q: Find the expression of the general term of the sequence given by: 32 2 4 8 16 1, 2'6' 24' 120’ 720

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Q: Find the volume V of the solid S that results when the region bounded by y = x2, y = x, x = 0 and y ...

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Q: Given the triangle below, find sec(0). Enter an exact answer in fraction form.

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Q: 4. f(x) = a = 0 x2-4x %3D x2+4x x?-3,xミ-1 5. f(x) = {x- 1, x>-1 こa=-1 %3D

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Q: Related Rates - Rectangles Mar 20, 9:02:57 PM Watch help video A rectangle has a length of 7 inches ...

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Q: Calculate the arc length of y = - x² - In x over the interval [1, 8e]. %3D

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Q: Evaluate the triple integral. (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x2...

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Q: f(x) =a= 2 3. %3D THE IA

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Q: Find (f-1)'(a) for f(x) = ーX-3 when a = 3x +2 (Enter an exact answer.) Provide your answer below: ((...

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