If y = 5x + 8 find 8' X dy dx at x = 1.

Q: For the following differential equation d²y dt² + 4y = 1 cos (21) a. Find the general solution b.…

A: The given differential equation is

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 5 r…

A: r=5θ,π2≤θ≤2π

Q: Use the tangent line to the curve  x7 + y2  =  x + y  at the point (1, 1) to approximate the…

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Q: Find the domain of the function. f(x)= x-1 X+2

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

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Q: 9. If f(x)=x²-2x+7, evaluate each of the following

A: The given function is To find:-

Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5,…

A: Equation of plane : and equation of cylinder : Find the volume of the region in the first octant…

Q: The populations of Towns A, B, and C vary exponentially with respect to time. The population of…

A: The populations of Towns A, B, and C vary exponentially with respect to time.1.The population of…

Q: Seperate the variables and solve the equation (dy/dx)=-e^(x-y). Use the initial condition x=0; y=0…

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Q: A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see…

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Q: Consider the integral approximation T20 of fo 2e-4 dx. Does T20 overestimate or underestimate the…

A: Here And Now,         ..........(1)

Q: Solve the second order. 1. eq Y Ý + Y

A: The given differential equation is

Q: (a) Find parametric equations for the line segment that joins the point P(-1,-4, -3) to the point…

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Q: Find the absolute maximum and absolute minimum of the following function on the given interval. ƒ(x)…

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Q: 1. Find the derivative of: a. y=(x-1/x+1)^2

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

A: Recall:Area of the resulting surface rotated about the x-axis :If the curve y= f(x) ,…

Q: Find d'y dx² if f(x) = 3x³ (√x − 2).

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Q: Find the inverse matrix where A = 1 -1 2 -3 -3 1 2 -3 -3

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Q: Find the domain of the function. X-5 X+9 f(x)=

A: Rational function is defined if the denominator is not equal to zero.

Q: -4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

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Q: Question 6 Calculate the resultant of the forces shown in the concurrent force system. 6N 40% 30N…

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Q: Sales The profit for a product is increasing at a rate of $5600 per week. The demand and cost…

A: The profit for a product is increasing at a rate of  per week.The demand and cost functions for the…

Q: Let g(x)-3x³-20x² Find the relative maximum and minimum values of g. Also find the intervals on…

A: The given function is

Q: Find the solution of the following problem. y' - (x + y)(x + y +3) = 1

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Q: Z₁ cos# = 2 V₁ 1 V +(x-2- sin e Z₁ cos Z₁ X + V₂ V₂ cos 9) +1/+ Z₁ 1 V. cose V 2 -sin 0 +

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4+x² - y2…

A: The given function  and region R

Q: Given the following integral and value of n, approximate the following integral using the methods…

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Q: 3. Consider the curve which is the graph of the equation r³+y³ - 3xy = 0. Graph this curve using…

A: In this question, we will find the implicit derivative.

Q: Find f. f(t) f'(t) = t³ + -/-/7₁ t5 t> 0, f(1) = 4

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Q: describe what you would have to do to your graph of f(x) to sketch g(x)= (x+1)^2-4(x+1)+3

A: The given function is .The aim is to describe how to sketch the graph of the function using the…

Q: b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Evaluate the integral by converting to polar coordinates. 2 √8-y2 S² S Y 1 √1+x² + y² dx dy= = 16pi

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Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph

Q: Describe the x-values at which the function is differentiable. x² y = x² - 49

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Q: Roberto has plans to build a tree house in his backyard. He takes measurements from the ground and…

A: Here,

Q: Determine the horizontal asymptote of the graph of the function. x3 - 5x2 +x-2 x²-20 f(x)=- Select…

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Q: If what does the following integral equal? -15 -50 [9f(x) + 2g(x) - h(x)]dx = -15 |_| f(x)dx = 15…

A: The integrals are given asTo evaluate: The value of

Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

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Q: Evaluate the following integral using trigonometric substitution. x² √√64-x² S dx

A: I=∫x264−x2dx

Q: Find the total differential. 8x + y 3z - 2y dw = W = 8 3z-2y dx + 3z- - 4y - 16x (3z-2y)² Jdy + (7…

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Q: Find aw/as and aw/at using the appropriate Chain Rule. Values Function w = y³ - 2x²y s=-3, t = 6 x =…

A: To find  by using the appropriate Chain Rule.Function: Values: To evaluate each partial derivate at…

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: Order is the highest power of the derivative Degree is the power on the highest power of the…

Q: dy d²y Find and dx dx² x = t² + 2, y = t² + 3t dy dx d²y dx² For which values of t is the curve…

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Q: Step 3 Write the two binomial factors so that the first term of each factor is x and the second…

A: To write the complete factorization of

Q: Give the partial fraction decomposition for the following function. 2 x²-2x-8 2 2 x-2x-8 ||

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Q: 3. Consider the circle as a vector-valued function r(t) = cos(t)i + sin(t)j. Calculate limt→+∞ r(t)…

A: Find the limit

Q: Show that the function y= x ln x is a solution of the differential equation xy" - y' + (1/x) y = 0.

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