Find the following limit. lim x-x 2+ x - 4x³-4 5 x³x²+1 Number

Q: Suppose Use this to compute the following limit. Limit= Number What Theorem did you use to arrive at…

A: Snadwich TheoremSqueeze Theorem:  If g(x)≤f(x)≤h(x)  for all x in an interval containing a point…

Q: K A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges…

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Q: 8. Use the limit comparison test to determine the convergence of the following series; state what…

A: See this solution in below.

Q: Given lim f(x) = -5 and lim g(x) = -12, evaluate lim [5f(x)-2g(x)]. X→ 11 X-11 X→ 11 O lim…

A: Given that: limx→11f(x)=-5, limx→11g(x)=-12

Q: Boyle’s Law says that the volume V of a gas atconstant temperature increases whenever the pressure P…

A: Given: Volume and Pressure are inversely proportional. P=14.7lb/in2when V=1000 in3 To find: V when…

Q: 14. A rock is thrown vertically into the air, after t seconds the height of the rock in feet is…

A: Given query is to find the the velocity of the rock.

Q: Find the limit of each of the following sequences, using L'Hopital's rule when appropriate. √n Vn+1

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Q: Determine the degree, order, and whether it is linear or non-linear (y") ³-4y²=105x

A: Determine the degree,order, and whether it is linear or non linear

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

A: By using synthetic division method the solution of given problem is as follow

Q: 2. Find the 2nd derivative of sin (x²-1) y *2cos(x^2-1) 4x^2 tan(x^2-1) 2cos(x^2-1) + 4x^2…

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Q: Derive a Differential Equation that is free from arbitrary constants: y = Ae²x + Bxe²x

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Here we can create the required polynomial function in the below steps.

Q: 80 LUPTATE 40 You can expect Interstate 40 to be A. north B. south C. east O D. west 80 40 of…

A: According to map's direction indicator below side is in souh direction and upper side is in west…

Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4eY - x²y² - 3x)dy = 0 when…

A: uation Given differential equation of the formMdx+ Ndy=0

Q: Sketch the region bounded by the curve x² - 2 = y and the line x = y + 2 and find the volume of the…

A:

Q: Sketch the region bounded by the curve x 2 = y and the line x = volume of the solid generated by…

A: solution:-the region bounded by y=x2-2 & x=y+2revolving around y=1

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: lim 1 - cos(sin(³-1)) 73 - 1

A: As per the instruction, we will be answering the first question. The graph of y=1-cossinx3-1x3-1.

Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: If bn = determine whether this sequence converges or 271 Convergent, give the limit of this…

A: we know that sequence is defined as the set of natural numbers N and X any set, then a function…

Q: Which of the following equations OA. (2x sin y + y)dx + (x² cos y + x)dy = 0 OB. 1 dx-dy-0 y O E.…

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Q: 7. Use the integral test to determine the convergence of the following series: ∞ n=2 n ln n น

A:

Q: Given the plane л: 2x + y - 3z - 2 = 0, and the lines l₁: 2 - Z-4 y-1 x+1 x==¹=24 and ₂: *1 = y…

A: (b) Given two lines l1: 2-x=y-12=z-43 write it in standard form…

Q: f(x)=4ln(4x+6ln(x)), find f'(x).   f'(x)=

A: Given query is to find the derivative of the function using chain rule.

Q: A community skating rink is in the shape of a rectangle withsemicircles attached at the ends. The…

A: Given data, The length of the rectangle given is 20 ft less than twice the width. The thickness of…

Q: graph each equation.   y = 2x

A: Given data:- The given equation is, y=2x

Q: Find dx dx || by implicit differentiation. 6x² + 7xy - y² = 8

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the…

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Q: Find the value of the constant b that makes the following function continuous on R. 8x - 26 f(x) =…

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Q: Geometry A wire of length x is bent into the shape of asquare.(a) Express the perimeter p of the…

A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

Q: Find the area bounded by the curves x y = 8 (in green), y blue) and the line 3y sliced pizza? 2 =…

A: Let's find area of the sliced pizza.

Q: Evaluate the derivative of the following function. 1) 6x H(x)= (5x +

A:

Q: Given the differential equation: 2 y' + ²y = 6x²

A: To choose the appropriate method to be used to solve the given DE. Method 5: Exact Equation Method…

Q: Which of the following equations can be made into a linear differential equation? A. (x² + xy)dy -…

A: On solving this we will get

Q: Consider the function f(x)=eXx. Select all that apply. Select 3 correct answer(s) f(0) is positive.…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

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Q: A solid lies between planes perpendicular to the y-axis at y = 0 and y = 1. The cross-sections…

A:

Q: 2. 8[][

A: The objective of the question is checking the convergence or divergence of the given series.

Q: Which of the following equations is NOT a variable separable differential equation? A. 2xydx + (x² +…

A: To find the equation is not variable separable.

Q: Find a general formula for f(n). ƒ(x) = (x + 7)−¹

A:

Q: (c) Let y = (In x)2. Compute y' by using logarithmic differentiation.

A: The given function y=ln x2x We have to find the derivative of y using logarithm differentiation.

Q: Given the following functions: f(u)=u^5/2 and g(x)=x^6+1. Find f(g(x))= f′(u)= f′(g(x))= g′(x)=…

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Q: For the function f(x) = 5x² 2x, evaluate and simplif f(x+h)-f(x) h 11

A: f(x)=5x2-2x hence f(x+h)=5x+h2-2x+hf(x+h)=5x2+5h2+10xh-2x-2h

Q: 1. Find the limit. lim X-5 lim x-5 2 √x +11 -6 x-5 2 √√x+11 -6 X-5 =

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Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

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Q: Find the area between the curves (Hint: Your answer will be in terms of a.) The area is f(x)=x and…

A: area is=a3/6

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O A. O B. O U ev O D.y O E.…

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Q: Solve for the value of C in the equation: A. 1 B. 2 C. 3 D.-1 (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y²…

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Q: Solve for the value of C in the equation: O A. -5 B. 5 O C.-4 O D. 4 O E. None of the Choices dx…

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Q: Let P = 1x, y2 be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the point…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…