3. Find the area of the region inside the circler-3 sine and outside the limacon r= 2 - sine. Sketch the polar graph.

Q: Evaluate the integral / (6x + 18y)dx + (12x – y)dy along the parabolic arc y = r from (0,0) to (1,…

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Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: Consider a wood beam (see figure) carrying a uniform load of 20.5 kN/m (which includes the weight of…

A: answer is in next step

Q: f(x) 7xe-x, y = 0, 0 <x < 1 ketch the region bounded by the graphs of the equations. 3- 2- y 3

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Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: Find f, and f and evaluate each at the given point. F(X, v) = arctan). (2, -2) f,x, y) = %3D X, v) =…

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Q: sider the function f(x) 3x on the interval |- 2, 2]. Find the average or mean slope of the ction on…

A: Topic:-  derivatives

Q: ?

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Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i+11 sin(t)j+4tk;…

A: Given problem:- Find the curvature and the radius of curvature at the stated point.   r(t) = 5cos…

Q: 2. Find an equation of the plane containing the point P (0,-.) and the line determined by the two…

A: Equation of a plane P containing a line of intersection of two planes P1,P2 is given by, P=P1+λP2

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

A: Given problem:-

Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: Given the function: x2-4 if x 2 f(x) = , 2-x if x = 2 What should be the value of k so that f is…

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Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), v (PR), and V(PS) are…

A: Given PQ=3i+2j-k PR=i-2j+3k PS=i-j+k. Volume of parallelepiped =[PQ PR PS]…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5…

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Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

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Q: What is the area of the region bounded by the graph of r = 4 cos 20? Choose two (2) correct answers.…

A: Let's find.

Q: Consider the matrix 2 -1 A =| 1 3 -1 -2 2

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Q: On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric…

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Q: What is the differential equation whose solution represents the family y = Ae3x + Be4x+Cxe4x? O…

A: Given problem:- Find the differential equation whose solution represents the family y=Ae3x +Be-4x…

Q: | x(x + 10)" dx

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Q: Describe the graph of the equation. r = (7 – 21) i + 10r j | O It is a line in 2-space through the…

A: The given equation is: r(x,y)=(7-2t)i+10tj⇒x=7-2t    y=0+10t

Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: Match the equation with its graph. 16 56

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Q: Find V· (V × F), if F(x, y, z) = 5e**i+ 5xe®j – 7ev³k. V· (V × F) =

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Q: Fibe the graph of the equation. = (7 – 21) i + 10tj r = O It is a line in 2-space through the point…

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Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = i Di + ( Dj + ( i )k

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Q: (4x-3) find dy/dх y = (2х-7)6

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Q: Using an appropriate substitution, cos x-sin x the integral 3. dx equals: 0 cosx+sin x O none of…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal.…

A: Given that,      z=19xey-10ye-x

Q: Determine the vector field of F. F(x, y) = yi – xj

A: Given that,  F(x,y)=yi-xj

Q: Directions: Compute f'(3) for each of the following function. Then connect item A to item B by using…

A: We have to find the value of f'(3).

Q: Let 7 (t) = Find a parametric equation of the line tangent to 7(t) at the point (– 27, – 44, 1.792)…

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Q: Evaluate the triple iterated integral. xyz dx dy dz Jo

A: To evaluate the triple integral.

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: Describe the graph of the equation. r = 10 cos ti + 8 sin tj – k O It is an ellipse in the z = – 1…

A: Given that       r = 10 cost i + 8 sint j - k

Q: Solve the following differential equation step by step! y" – 2y' + y = x² + 1

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: Suppose the function f(x) is an odd function and lim, f(r) = 27. Use this information to evaluate…

A: For an odd function f(-x) = -f(x)

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. π 1 sin -x cos? 1

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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: Establish the identity. 3 csc0 4 cos 0 = 7 cot 0 sec 0 sin 0 Write the left side of the identity in…

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Q: Find V. (V x F), if F(x, y, z) = 3e"i+ 7xe"j – 3ek. V.(V × F)

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Q: Solve the initial value problem y′′−10y′+50y=0 for y(0)=1 and y′(0)=5. After getting the equation…

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Q: If f(x) = u(x)t(x)w(x), then f'(x)= a) u'(x)t'(x)w'(x) b) u'(x) + t'(x) + w'(x) c) u(x)t'(x)w'(x) +…

A: Solution ) f (x) = u(x) t(x) w(x) To differentiate use product rule  [ Formula d/dx ( f (x) . g(x) )…

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

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Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: 2) Find and of the following equation then simplify whenever possible. dx x = 1+ Sin t y = Cos? t

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