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Q: 1. Find the general solutions to the differential equations: y" + 5y' - 6y = 0 y" + 6y' + 9y = 0 2...

A: characteristic equation is: r^2 + 5r - 6 = 0 (r+6)(r-1) = 0 -> roots are 1 , -6 So the solution i...

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence con...

A: Given: an=en4n given series is geometric series whose first term is e4 and common ratio is e4 we kno...

Q: Find the exact length of the curve. x = 6 + 12t2, y = 8 + 8t, 0sts1

A: If x=f(t), y=f(t) on [a,b] then length of curve is L=∫abdxdt2+dydt2dt

Q: if F(x)= f(g(x)), where f(-2)=8,f'(-2)=4, f'(5)=3, g(5)=-2,g'(5)=6, find F'(5)

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Q: Consider each matrix in Exercises 5 and 6 as the augmented matrixof a linear system. State in words ...

A: Given augmented matrix is 1-640-102-7040012-300316

Q: Using the slope you found in question 1, find the equation of the tangent line ) = 3x² at x = 2. to ...

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Q: Find the derivative.

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Q: angle between A and B.

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Q: Find a formula for the nth term of the sequence:

A: We have to find the formula for nth term of the sequence: 51,82,116,1424,17120...... Here we have to...

Q: Taylor polynomials Find the nth-order Taylor polynomial for the following functions centered at the ...

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Q: 3) Show that (f • g)(x) = (g • f)(x) = x. f(x) = 4 – 3x g(x) =(4 – x)

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Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: Use the definition of the derivative to determine the derivative of the following function: f(x) =(...

A: Solution by definition of derivative :-

Q: Consider the function given by ?(?) = 18x^2 ...

A: Consider the given function fx=18x22x-92

Q: Evaluate the following definite integral. Show all intermediate steps. ∫12 [ 2xe^(x^2+1) + (9x^2+1...

A: Explanation is given below...

Q: I’m working with the linear function f(x) = 3x + 5 and I do not need to find f-1 in order to determi...

A: f(x)=3x+5 and if we will calculate fof-1 then we must have calculate f-1 at first. Let y=f(x) then x...

Q: please see attached

A: From the given graph, it can be concluded that y = 1 at x = 0 (where graph crosses y-axis).

Q: x/42 Evaluate x tan (14x)dx. /42 x tan (14x)dx = Type an exact answer, using t and radicals as neede...

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Q: Sketch a graph of the polar equation r = 3 sin 2 and find the tangent line(s) at the pole (if any).

A: We have to sketch a graph of the polar equation r=3sin2θand then we have to find the tangent line(s)...

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: The radius of a circular oil slick expands at a rate of 5 m/min. (a) How fast is the area of the oil...

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Q: A group of students went on a field trip to the zoo. 12 students went to the tiger exhibit. 4 studen...

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Q: 3. Evaluate derivatives of following. Tell me WHICH RULE vou are using and CLEARLY SHOW your use of ...

A: (a) Given data: The given expression is y=30/x9-20tan(x)+(x5)1/2+10ex+ln(4000). The derivative o...

Q: Consider the following functions. f(x)= 1/3x^2-3/4x g(x)=1/2x+5/6 h(x)=1/4x^2-5/8x+2/5 Part a. Amari...

A: We have f(x)=13x2−34xg(x)=12x+56h(x)=14x2−58x+25

Q: In problems 11 and 12 determine by inspection at least two solutions of the given initial-value prob...

A: (11) Given differential equation is y'=3y23 and y0=0. Given differential equation can be written as:...

Q: Use the Green’s Theorem area formula given above to find the areasof the regions enclosed by the cur...

A: The give curve is circle. The parametric form of circle is, r(t) = (a cost)i + (a sint)j. Here, x = ...

Q: In Exercises 1–10, assume that T is a linear transformation. Find the standard matrix of T.

A: Given that T:ℝ2→ℝ2 is linear transformation such that T rotates the points about the origin through ...

Q: let hG) = f(x) %3D where f(-3) = 7, f'(-3)= - 9, g(-3) = -2 and gʻ(-3) = 1. What is b'(-3)? %3D %3D

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Q: An arch in a church, having a parabolic shape, has a height of 28 feet and a base width of 34 feet. ...

A: Given: An arch in a church, having a parabolic shape, has a height of 28 feet and a base width of 34...

Q: If tan t=9/2, what is tan(t−π) ?

A: Given, tan t=92

Q: Evaluate the following indefinite integral: ∫ (5x)/((x+5)^3) dx

A: Given Integral I=∫5x(x+5)3dx Take the constant out from the integral as : ∫af(x)dx=a∫f(x)dx I=5∫x(x+...

Q: The function f(x) = √x is one-to-one. For the function,a. Find an equation for f -1(x), the inverse ...

A: We are given that the function f(x)=x is one-to-one. For the function(a) To find an equation for f-1...

Q: dy/dx=y2/3

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Q: We take a milk carton out of the fridge and place it on the table at room temperature. We assume tha...

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Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable. (I...

A: Given function ft=2t+1t

Q: USE L' HOSPITAL's RULE TO EVALUATE.

A: Given data: The expression for the limit is limx→-13x3+4x2-x-22x3+5x2+4x+1. Substitute the given...

Q: Write an equation for the function illustrated in the graph below.

A: The given function is a piecewise function. It has different functions in different domains. The do...

Q: Suppose the radius of a sphere are expanding at a rate of 6 inches per minute.How fast is the volume...

A: Let us suppose the radius of sphere be R. Given that : dRdt=6 incheminute. Radius=Diameter2=122=6...

Q: What are all the values of x where the original function f(x) (no shown) has a local (relative) maxi...

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Q: Use a graphing utility to graph the equation and show that the given line is an asymptote of the gra...

A: Given, Polar equation r=2-secθ and asymptote x=-1

Q: Chicago has a temperature of -7 degrees Fahreneheit ( °°F). It is colder in Boston than in Chicago. ...

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Q: True or False. The product of two increasing functions is increasing. Clarify your answer.

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Q: Problem 6: Find the equation (in symmetric form) for the line of intersection between the following ...

A: Solution :-

Q: A street is 75 cm long and needs to be cleaned. The street cleaning vehicle has wheels that have a d...

A: Length of street to be cleaned=75 cm Diameter of cleaning vehicle=1m We know , 1m=100cm So, diameter...

Q: a. Express the volume of the wedge in the first octant that is cut from the cylinder y2+z2=1 by the ...

A: a) Express the volume of the wedge in the first octant that is cut from the cylinder y2+z2=1by th...