a) Use the indicated test to decide if the giv 1) En=1 (1 (Root Test)

Q: dx = 8xt* dt

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Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle ab...

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Q: Evaluate each limit. f + 5 lim S2 1 + Vr + 5

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Q: Evaluate the indefinite integral

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Q: Find the thousandth derivative of  f(x)  = x e-x

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Q: Explain the main property of tangent function?

A: The tangent function is an odd function, and its graph is symmetric with respect to the origin over ...

Q: sketch the shifted exponential curves y = 3x + 2 and y = 3-x + 2

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Q: Simplity b-[b-Ca+b) - CB-Cb-a-b)J+2a]

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Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

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Q: Graph each side of the equation, tan x = sec x(sin x - cos x) + 1, in the same viewing rectangle. If...

A: Given Data The equation is tan x=sec x(sin x-cos x) +1.   Solve the right hand side of equation tan ...

Q: Evaluate using the Squeeze Theorem. lim cos θ cos(tan θ) θ→ π/2

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Q: If C(m) represents the cost (per month), in hundreds of dollars, of a car after m months on the mark...

A: Given, C(m) is the cost of car after 'm' months on the market.

Q: Insert either <, >, or = in the blank to make a true statement 17/18 . 18 /17 …… 50/60 -5/6.

A: And

Q: Consider f(x) = xe−kx for k > 0. Find the relative extrema and the points of inflection of the fu...

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Q: Determine the order, degree, ordinary or partial, linearity, and unknown function and independent va...

A: Consider the given differential equation: Here the objective is to determine the order, degree, ord...

Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asympto...

A: Given 

Q: Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

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Q: Determine whether the given statement makes sense or does not make sense, and explain your reasoning...

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Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw i...

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Q: Find f + g, f - g, fg, and f/g and determine the domain for the given function : f(x) = 5 - x2, g(x)...

A: Given functions,  f(x) = 5 - x2  g(x) = x2 + 4x -12 We have to find f + g, f-g, fg and f/g. And the ...

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =...

A: We compare  f(x) = 3x2 - 12x + 1 with  f(x) = ax2 +bx + c  So, a=3, b=-12, c=1   

Q: Arc length by calculator a. Write and simplify the integral that gives the arc length of the followi...

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Q: The polynomial function f(x) = -0.27x3 + 9.2x2 - 102.9x + 400 models the ratio of students to comput...

A: Degree of f(x) is 3 and lead coefficient is -0.27  Because of the negative lead coefficient, the gra...

Q: Evaluate the limit.

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Q: Find the unit vector in the direction of V. V = -6.7i + 3.9j

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Q: Find the point at which the line intersects the given plane. x = 4 − t,  y = 2 + t,  z = 3t;    x −...

A: x = 4 − t,  y = 2 + t,  z = 3t;    x − y + 5z = 15 We need to find the point at which the line inter...

Q: The cost, in dollars, of producing z units of a certain item is given by C (z) = 0.03z3 – 10z + 200....

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Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes ...

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Q: Give a practical formula for computing the principal unit normalvector.

A: To define: Principal Unit Normal Vector. To write the formula for Principal Unit Normal Vector.

Q: Use any method to evaluate the integrals. Mostwill require trigonometric substitutions, but some can...

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Q: Find the solutions of the following clairaut differential equations.

A: The clairaut differential equation is, y = xy’ + (y’)2 ……(1)   Differentiate the above equation with...

Q: Rewrite y = 96(0.38)x in terms of base e. Express the answer in terms of a natural logarithm and the...

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Q: Find the general solution to the given Euler equation. Assume x > 0 3x2y" + 4xy' = 0

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Q: Let P and Q be points in R2. Show that a linear map G(u, v) = (Au+ Cv, Bu+ Dv) maps the segment join...

A: Let P and Q be two points in R2. We have to show that a linear map G(u, v) = (Au + Cv, Bu + Dv) maps...

Q: Determine whether the given differential equation is separable. (xy* + 8y*) dy - 2ydx = 0

A: Given: To determine whether the given differential equation is separable.

Q: Sketch the graphs of the rational functions y = x2 + 1/x

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If true...

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Q: Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote posit...

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Q: ty?. Evaluate lim 2,3 (1, y, z)(1, 1, –1)

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Q: You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller ...

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Q: Use the Product Rule twice to prove that if f, g, and h are differentiable functions of x, then

A: Let us assume f(x)*g(x) together. and h(x) separate.  Then apply the product rule  

Q: Find the equation of the plane contains the lineX+1/2 = Y/3 = Z-1/4and the line of intersection of p...

A: We have given the line of intersection of planes; x + 2y - 2z = 6 , 5x - 2y - z = 0 and line; X+1/2 ...

Q: Use a convergence test of your choice to determine whether the following series converge.

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.     ...

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.