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Q: Evaluate the following indefinite integral. dx

A: Here is the solution

Q: Find dy/dx by Implicit differentiation. x = 9 In(y-15), (0, 4) dy %3D Find the slope of the graph at…

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Q: The volume of the solid obtained by rotating the region enclosed by y = eSz + 2, y = 0, T = 0, I=0.4…

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Q: "(x) If t(x) = Vx find ť'(x)" -2x O 2x -1/2x O 1/2x O None of these O o o o

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find an equation of the tangent line to the curve y = x3 – 3x2 + 5x that has the least slope.

A: Given

Q: %3D Find the derivative of y = Vsinx COS I 2sin z 1. -sin z H S00 5.

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Q: Solving Separable Equations: 1. dy - x-5 dx y2 2. = dx 3x²(1+ y?)

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Q: Find the area of the region that is enclosed between y = 6x² – 2³ + ¤ and y = z² + 5z. The area is

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Q: 2. Detemine if the ollowing integral converges or diverges. If the integral converges, find its…

A: Given problem:- Determine if the following integral converges or diverges. If the integral…

Q: Use algebra and the properties of limits as needed to find the given limit If the limit does not…

A: We need to evaluate limit.

Q: Use substitution to find the indefinite integral. 6x + 5 -dx (9x? + 15x) 2 S 6x + 5 xp. 3 (9x? +…

A: The detailed solution is given below Thank you

Q: Determine if the following integral converges or diverges. If the integral converges, find its…

A: To determine whether the given integral converges or diverges.

Q: (3)" n=0 _n!

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Q: 2. y =,x = 1, x = 4, and y O is revolved about the y – axis. (Answer: 247 c. u. )

A: Given: y=4x, x=1, x=0 and y=0   The bounded region is as shown below.     Apply the cylindrical…

Q: Evaluate the integral |- 5x + x3 - 2 x5 dx 3

A: Topic:- integration

Q: Find the limit. lim ---X +4 Step 1 1 x+ 4 as x approaches -4 from the left. Note that we cannot…

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Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

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Q: 1.1 1) lim (2) x3+8 X→-2

A: Given query is to find the limit nofnthe expression

Q: 5- X dy + y dx =X cosx dx dy 6- -zy メ

A: First order differential equation: Consider the first order differential equation…

Q: Find the Indeftnite Integral and check the result by differentiation. (5x) Step 1 To obtaln the…

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Q: Geometric Sequence A. Find the indicated terms of the following geometric sequences. 1. 12, 6, 18,…

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Q: Show that the function f defined by (x, y) = (1, –1) f(x, y) = r? + y (x, y) # (1, –1) x + y is not…

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Q: 3. A girl is flying a kite on a string. The kite is 120 ft. above the ground and the wind is blowing…

A: To solve this problem we use pythagorous theorem.

Q: A ldentifcation. Tel whether the folowing sbligve triangle is Case , Case 2, Cae 3, Case4or Case…

A: The question is not clear

Q: Find the Average Rate of Change of the following function ver the interval [1, 7] (That is, from t=…

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Q: Find the area of the region between the curves y = æ and y = Va. Area between curves

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Q: An open-top rectangular box is being constructed to hold a volume of 150 in?. The base of the box is…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- = 5 sin t and 0= 5t = ( 5 cost)u,…

A: Topic:- application of derivatives

Q: The point (1,3) is on the graph of x* . y? + 5 · y = x* + 23. Find the slope of the line tangent to…

A: Please follow the next step.

Q: The following integral may be solved using substitution. Choose a function u that may be used to…

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Q: r(10,3,3) dx (1,1,1) dy dz. - -

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Q: Write a in the form a = a-T+a,N at the given value of t without finding T and N. )3 (7 e*cos t)i+ (7…

A: Given that;                      a(0)  = atT + anN     Let's   Find  the value of at and an.

Q: Q2: State and prove the first isomorphism theorem.

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Q: 4 Evaluate f². dx 4-x*

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Q: Find the volume oF the solid obtained by rotating about the x-axis the region by y= x' and the lines…

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Q: a). Find the specific solution to the 2nd order non-homogeneous differential equation d²y dy 12y =…

A: a)The given differential equation,d2ydx2-dydx-12y=30x

Q: A chemical factory tank stores an amount of liquid. After it has started to drain, it has a given…

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Q: Exercise 14.5.5 dy if y is defined implicitly as a function of z by the equation dz To find 2 + ry –…

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Q: Use the chart below to find the average rate of change of the function f(x) over the interval given.…

A: Our Aim is to find the average rate of change of the function f(x) over the interval given.

Q: Find the given limit. lim (-x + 2x- 1) x-5 lim (-x +2x-1) = (Simplify your answer) X-5

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Q: Differentiate each function by applying chain rule. Match each item to a choice: y = x(x² + 3)² f…

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Q: 4-In any clements is the only hilpolent elements O ac-b)= C-ajb= - Cab) O C-a) (-b) =ab %3D %3D

A: 1.  We have a(-b) + a.b =a.(-b+b).     ( Distributive law )                    = a.0…

Q: 3. y? = -x ,x² + 3y + 4x + 6 = 0

A:

Q: 7. Find the exact x-value where the function f (x) = x +In (7„² – 1) attains a maximum value. An…

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Q: |+ 3t -dt 11t Simplify the integrand by dividing eac .5 |+ 3t -dt = 11t |dt Type an exact answer.)

A: Given:∫1+3t511tdt

Q: 1-cos 4x Find the derivative of y sin 4x

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Q: Find the plane determined by the intersecting lines.

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Q: 1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If…

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Q: Evaluate the following indefinite integral. f11 de dx = (Type an exact answer.)

A: To find out the integration.

Q: Write an equation for the polynomial graphed below 5 4 3 1 2 -1 -1 2 3 4 5 -5 -4 -2 - -3 -4 -5 +…

A: topic- polynomials