1 EVA LUATE ECs) OF THE DIFF ARD 4(0)-0. dy dt² dt

Q: Find the most general antiderivative or indefinite integral. csc 30 de csc 30 - sin 30

A: The objective is to evaluate the integral.

Q: V y-2+1 dy

A: Please see the answer below.

Q: Fove that y = ln|| is a solution to 1+e-22 - xey-x² . Use the initial values x = 0 and y = 0.

A: Given query is to find the solution of the differential equation.

Q: g(x) = e× In x12 g'(x)=

A: topic - derivative of a function

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: Both these questions can be solved by applying the concept of maxima and minima.

Q: Find the dimensions of a rectangle with area 216 m whose perimeter is as small as possible. (If both…

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Q: a) Find the degree 3 Taylor polynomial T3(x) for the function f (x) 4 ln(x) centered at the point a…

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Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: We have to find the increase of area

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: 1. (3x²+ 2y²)dx + 2xydy=0 2. (x- 3y + 3)dx + (3x + y + 9)dy = 0

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A: The vector v has,magnitude, v=2angle, θ=0°

Q: 1+cos4x 1. 1-cos4x -csc2xdx

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Q: Suppose the position of a particle is given by parametric equations x(t) = 2t2-1 and y(t) = 3t3. (a)…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 70 11 odometer. To find out how long this road is, you record the car's velocity at 10-second…

A: To find the length of the road, given velocity

Q: 11m Convert to its degree measure. 6.

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Q: Which of the following is 2 equivalent to tan x + cot x where x = -? 2 sin 0 2 sin 0 2 Option 1…

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Q: y dy J 725 – 16y 2.

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Question Using Trigonometric Substitution, evaluate: S e4*/1+ e2xdx Your answer

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Recall: v = can be written as v = ai + bj + ck , where i = , j = and j: . Let v = – 2i + 5j – 4k…

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Q: Note: you will need to find both the gener e homogeneous problem, and a particular so mogeneous…

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Q: Convert - 240° to its radian measure.

A: Given  240°

Q: The graph of fis shown. Evaluate each integral by interpreting it in terms of areas. y y= fx) 6. 0.…

A: Given query is to find the value of the integral.

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 u · (v x w)| to determine…

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Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

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Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

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Q: dx Assume that x= x(t) and y= y(t). Let y =x +4 and -5 when x= 1. dt dy Find when x= 1. dt

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Q: Find the maximum value of the function f(x) = x3 - 9x2 + 15x - 5.

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Q: 11.(Straightforward) Find a particular solution to each of these ODES by using the method of…

A: As you have asked for question 11 c only. So I am solving that only. Thank you.   Two solutions y1,…

Q: Find the Gauss quadrature rule for f(x)dx z wof(xo) + wif(x1) + wzf(x2). Nodes: Xo = X1 = X2 =…

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Q: uantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer…

A: Since we are given with the multiple number subpart answered according to the guidelines

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Question 12 V3 sin(0 + m) What are the solutions for the equation cos(o + 1) = 1,

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Q: Answer

A: As per policy, only first question is answered.  Please refer to the image below

Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X00 X-00 -5 + 2e-* f(x)…

A: The objective is to evaluate the limit.

Q: Use the position function s(t) --4.9+ 650, which gives the height (in meters) of an object that has…

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Q: Find the volume of the region lying above the cone o = and below the sphere p = 7. (Use symbolic…

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Q: The equation of the line tangent to the differentiable and invertible function f(x) at the point (5,…

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Q: vo Variables 4)dr + (2r. (2. 4x)dı

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Q: Simplify -3j 1234567+ 4j98765432 – 5j-32198765 + 6. What is the imaginary part of the result? O 2

A: Given: -3j1234567+4j98765432-5j-32198765+6

Q: Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

A: Find your answer below

Q: 2. Find the equation of tangent line and normal line to 3x y3 + 2y =1 at (0.2) (15 points)

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Q: Find Ay and f'(x)Ax for y = f(x) = 2x – 1, x= 3, and Ax = 3. Ay = (Round to four decimal places as…

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Q: Find the equation of the tangent line and the normal line of the curves at given point 1. 4x? + 9x?…

A: The given equation,     4x2+9x2=25, 2,-1

Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x° -…

A: Here we have to factorize the given cubic equation.

Q: Using the substitution Z=V x+2, the integral xVx+2 dx is equivalent to | 2°(?+ 2) dz 1 | 22?(z?+2)…

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

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