Using the laplace transformation table, evaluate the following, considering any other variable other than t as constant unless otherwise stated: c. L[(3e^2t)^2]

Q: Find the exponential function f(x) = Cbx whose graph passes through the points (1, 6) and (3, 24).

A: To find the exponential function satisfying the given conditions.

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Q: Find all the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + y² +…

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Q: lim,→-1 22²+2-1 2+1

A: See the answer below

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

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A: We have to choose the expression that represents the derivative of f at x.

Q: Which of the following is/are given by f'(c)? I. the slope of the tangent line to the graph of f…

A: Given problem:- Which of the following is/are given by f'(c) ? I. the slope of the tangent line to…

Q: 3/ 10. Find the arc length of the curve y = x/2 +4 from x = 4to x = 9.

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Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: Given: y2= 4ax

Q: ii. Given g(x)= x²+5 if x<-2 3-3x if x2-2 Find the following: 15 d. g(-2)= e. Determine with an…

A: gx=x2+5if x&lt;-23-3xif x≥-2

Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

A: Given a+b=120 .....1

Q: What is the derivative of x² + y² = 9 using mplicit differentiation? dx = xy dy dx = -xy dy dx dy dx…

A: Given query is to find the derivative of the expression.

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Q: Suppose a person is going up in a hot air balloon. The surrounding air temperature in degrees…

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Q: Graph the parabola. y=x+2x-2 Plot five points on the parabola: the vertex, two points to the left of…

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Q: Match the given differential equation with one or more of the solutions. (Select all that apply.)…

A: Substituting the given values of y in the differential equation

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Q: FIND y' ● 5x³3y5 = 4x²y + 10

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Q: For the following exercises, draw a typical slice and find the volume using the slicing method for…

A: Follow the procedure given below.

Q: Find the area of the region bounded above by y = sin(x) and below by y = cos(x 2 1.5 4 0.5+ X

A: Using horizontal /vertical strip

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find the area under the graph y = x 3 on the interval [1, 8]. 1 2 3 4 5 6 7 8 9 -NW 01 5- 4 3 2 क्त…

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Q: Evaluate: Express your answer in three decimal places. limx→8 √√x-2

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Q: 1. Find f'(x) for the following function. Then find f (1), f (0), and f(-4). f(x) = -9x+2 f'(x)=…

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Q: Given: ez + xy = 1 Find: əz ?х de dz dz 82 da 8z dz = = -I zez+y -eitz. -*e* ze²+y -ze**-y re**

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Q: 5. 1-cos2y 1+cos2y dy

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Q: For the function y = (x - 2) lnx, what are the two x intercepts, and between the two intercepts, is…

A: The given function is y=x-2lnx. For x intercepts we take y=0 and then we solve for x. If y''(x)&gt;0…

Q: Find y' y = e2x - e3x e4x

A: This question is based on diffrentiation of exponential Function.

Q: Which one of the following is the domain D for f(x, y) = ln (2²-(y-2)²) ? Select one alternative:…

A: The given function: fx,y=lnx2-y-22.We need to find the domain.

Q: Given f(x)=√ and g(x) = x. Which of the following integrals describes the area between the curves…

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Q: For the function f(x), whose graph is shown below in blue, find lim /(x). The red vertical dashed…

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Q: Find y. x³y³ + 3x = 8y³ +1

A: Given: x3y5+3x=8y3+1

Q: 10 Let u= (1, 2, -1) and v= (3,-1,2) be two vectors in Rª. Which of the following is a normal vector…

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Q: 4. √ (3x² + 4x − 5). 8(r³+2x²–5x+5) dx

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Q: Evaluate: lim, 1+ (-1)2 tan(x)

A: Evaluate the following limit

Q: Given f(x, y, z) = xV/x² - yz - - Determine of дz . O of дz of дz af дz of дz = = x² - у 2√x² - yz…

A: Find the derivative

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Q: Find the integrating factor by inspection then solve the following differential equation. Show your…

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Q: Evaluate the following integrals. (a) (b) Sx√4 x√4 + x² dx

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Q: Which function is Chain Rule most useful for? Composite function Polynomial function Logarithmic…

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Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1&lt; ln(n+1),for n&gt;2 so, 0&lt;(n^2)/(((3^(n+1))*ln(n+1))&lt;n^2/n^4=1/n^2,  since…

Q: Given the graph below, what can you say about the function at x = -2? -10 Not Continuous Continuous

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Q: Given the graph below, what can you say about the function at (-1,1)? Not Continuous Continuous

A: Here we have to find whether the given graph is continuous or not.

Q: Find the volume of the solid generated by revolving about the y-axis the region in the first…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

A: The given equation is homogeneous differential equation  (x-y)dx +x dy =0.            On…