Evaluate the integral. Give an exact answer. V2/2 7x2 dx = [Ans] 1-x2 Show your work separately and submit it using the assignment link Ise "pi" to represent the symbol Tt and write exponents using the"

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

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Q: 10. Let f(x, y) = x² + y³. Calculate the directional derivative of f in the direction of = (4, 3) at...

A: The given function is: f(x,y)=x2+y3Direction vector is:  v→=4, 3Given point:  P=(1, 2)

Q: Find the area of the part of the first quadrant that lies between the curves x+y-3 = 0 and xy = 1.

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Q: roblem 5: sing the method of shells, find the volume of revolution formed by revolving around the y ...

A: Given query is to find the volume of the solid generated. First we will find the boundary of the sol...

Q: Determine whether the lines L1:(x−22)/7=(y−17)/7=(z−19)/7 and L2:(x+15)/8=(y+22)/9=(z+22)/10 inter...

A: NOTE: Refresh your page if you can't see any equations. . the first line is  write the given line i...

Q: 5. In problems 1-5, by elimination the constant 'a' and 'b' obtain the DEs for which the following f...

A: Given:- y =A sin(A+B)  To find:- Eliminate arbitrary constant A and B obtain Differential equation

Q: Give an example of a definite integral which has value 2022. Only answer is required.

A: Example of a definite integral has value 2022.

Q: 4. Let V(t) be the amount of air in a balloon at any time t, find out whether the balloon is being f...

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Q: 3. If g(x) = x4 – 2, find g'(1) and use it to find an equation of the tangent line to the curve at t...

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Q: Evaluate, thus Is 27- 5) Calculate the Taylor polynomials T2 (a) and T3 (x) centered at a = a of the...

A: Taylor polynomial is given as                                                                   Tn(x...

Q: Find the value of a and b such that the function g(x) is continuous. x 3

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Q: 1. Find the volume of the solid obtained by rotating the area in the first quadrant bounded by y = T...

A: Given that y=x2, x=0, y=2-xaround the line x=1find the volume 

Q: Which angles have the same sine value? and 3. O T and 3 3 o 4T and 3 - 3 and 3 3

A: As we know that from the trigonometric identities; 1). sinπ+x=-sinx2). sinπ-x=sinx   And 3). sinπ3=3...

Q: 3. The disk and cylindrical shell methods for calculating the volume of a solid of revolution always...

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Q: (1-xy)^-2dx+[y^2+x^2(1-xy)^2]dy=0

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Q: (1 1 1) \ Find the co-factor matrix of | 2 4 \5 8 9. Find the adjoint of matrix A if A = d)

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Q: xdy – ydx – /x2 – y²dx = 0

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Q: Find the length of the curve r(t) (e" cos(2t), e" sin(2t), e"), -2 sts 2 %3D

A: I am attaching image so that you understand each and every step.

Q: 8(x – a) + 8(x + a)

A: Topic:- calculus

Q: Evaluate Ln(-5.3- j2.4) O 4.3143+ j1.0541 O 1.7610 – j2.7164 O -1.2232+j1.9883 O -2.6170 - j3.5246

A: First express the given rectangular point into polar form then using following identities find the U...

Q: Evaluate (sin t + 1)-1 dt A) sin t - sec t + C B tant + sec t +C (©) tant - csc t + C D tan t - sect...

A: Topic:- integration

Q: O Q 14. Choose the best answer. Find the value of the remaining side of the triangle a = 11, 6= 6, C...

A: Given :   a=11 b=6 C=14 degree

Q: If the terminal side of a contains the point (-3,4) and the terminal side of B contains the point (1...

A:

Q: For the following exercises, find the exact area of the region bounded by the given equations if pos...

A: Area between curves x2=y3 and x=3y

Q: Find the equation of an ellipse with center at (2,-2), vertex at (7,-2) and focus at (4,-2)? O (x + ...

A: We have to find the equation of ellipse

Q: Let RR be the first quadrant region bounded on the left by the yy-axis and between the graphs of f(x...

A:

Q: fo-Vin° e+2 ln² e+ln@ de

A: Here we have to solve the given Integral.

Q: A certain electronics manufacturer is making GPUS for gaming laptops (GPU stands for graphics proces...

A: Given an equation which represnt margin cost of x GPUs

Q: tan (log x) 2 dx 2 x(1+log*x)

A:

Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: solve with Laplace transform with x(0)=0

A: NOTE: Refresh your page if you can't see any equations. . take Laplace

Q: Obtain the solution of the following differential equations. 7. xy′ − y − 5x^4 − 3x^2 + 2x = 0

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Q: Find the vertical and horizontal asymptotes of the function f (x) = , where q (x) = (Va+5)(12 –x)² a...

A: Given problem:- Find the vertical and horizontal asymptotes of the function f(x) =1/g(x) where g(x)=...

Q: OVIS lhigaimad goinisab A awordz n El 2nibs to s(t) milov ad sd osvig 2000 W x(t)

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Q: 4. Find the exact arc length over the interval. b. x =y* from y = 1 to y = 4

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Q: Eliminate The Abritrary Constant

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Q: The length of the curve y = In(cos x), 0< x <:

A: To determine the length of the curve, y=lncos x, 0≤x≤π4.    

Q: It is known that the population of a certain country at time t is proportional to the people living ...

A: Given:- It is known that the population of a certain country at time t is proportional to the people...

Q: d Az3+7z+8, -4z3. dz d 3. (x)(3x² – 9) 2.

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Q: Evaluate the integral: ap- (A) Which trig substitution is correct for this integral? Or = 10 tan(0) ...

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Q: 30. A growing raindrop Suppose that a drop of mist is a perfect sphere and that, through condensatio...

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Q: An initial population starts out at 1,000. An hour later, the population is 2,000. Find how long it ...

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

A: Let's the check the answer by using differentiation   ddx2xx+153=23ddxx32+15x                       ...

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0), (0,2,0...

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Q: Let k be any integer. What expression generates all angles.coterminal with 135°? O 135° – 2Tk 135° 2...

A: We can find the conterminal angles as below

Q: ex-e2 1. lim x→2 x-2 x2 2. lim X0 sin 5x2 3. lim 5 cos 3x2-5 sin 8x2

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Q: B. EXACT EQUATIONS Find the general solution of the following differential equations dx (2) 3y sin x...

A: for the exact DE we have to make it separable DE so that we can separate the variables and then inte...

Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

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Q: y = x? + C,x + C2e¬*

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Q: Let 0 be an angle in standard position. If P(-1, 2) is a point on the terminal side of 0, what is th...

A: Topic:- trigonometry ratios