Find the area of the shaded region: y y = x - 15 x 20 10 y = x (4, 4) -6 2 4 6. (-4,-4) - 10 - 20

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A: The given function is f(x,y)=y2-x2 And the given constraint x2/4 + y2=1.

Q: dy dx + + 3y – 5x – e-t = 0 dt dt dx dy dt + x + y – 3 = 0 dt

A: Given: - The differential equation is, dydt+dxdt+3y-5x-e-t=02dxdt+dydt+x+y-3=0 To solve: - The solut...

Q: Detemine the x-values at whìch, 9水)= 2xー 3xー+X メt,xE - スxナラメー3x underined. Evaluate the linit ac xap...

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Q: 2x +3x-2 (i) lim 2х-1 1 +1 1) lim x+2 x+3 x-3

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Q: Radoc-Lactuan, I. et. al Analytic Geometry C. Show that the following sets of points belong to the s...

A: topic - coordinate geometry

Q: У(xtanx + Inу)dx + tanxdy 3D C

A: The given equation is; y(tan x+ln x)dx+tan xdy=0

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A: Topic = Limits

Q: Question 3: Evaluate the following limits, if they exist, by using the graph 3 -4 -3 -2 -1 3 -1 -2 -...

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Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9x)-cos(4x) +c Select one: True O False

A: topic- indefinite integral

Q: Function f(x, y) = 7x – 8y + 2xy – x² + y° -

A: we need to find the extreme points of f(x,y)=7x-8y+2xy-x2+y3  

Q: Find three positive numbers whose sum is 100 and whose product is a maximum.

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Q: Given the general solution to a differential equation and its initial conditions y(x) = C, e + C, e-...

A: Answer and explanation is given below...

Q: A. Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1 ...

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Q: tan(tan 3x)dx cos? 3xl

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Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How fa...

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: Given the differential equation y" - 4y' = 0

A: given differential equation is -  y"-4y' =0   

Q: Evaluate: 3 +4dy

A: ∫ 3y3y+4dy  

Q: Q5: Find the domain and range for:- (Answer two only) (1) F(x) = V5x + 10 (2) F(x) = 1+ x? x2+1 (3) ...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: 1. If {an} converges, then {an} converges (C). An+1 Suppose that limn→ 00 1n|= . Then E1 n2"a, conve...

A: We have to determine whether,  1. If {an}  converges, then {an2} converges. True /false? And  2. If ...

Q: (즈,-2)] ww m ie equation for this functic

A: topic - trigonometric equations

Q: QA Find 1 dx x2Vx? - a? Hint: Use x = a cosh(u).

A: Integral

Q: Another - the following. a) Set up an integral for the volume a solid torus (the donut-shaped solid ...

A: (a) To set: The integral for the volume of a solid torus. Given information: radii br and aR, a=7, b...

Q: Find the radius of convergence and the interval of convergence. (-1)*(x + 9)² k2 + 9 k=1 Radius of c...

A: In this question we have to find the radius of convergence and interval of convergence.

Q: Find the directional derivative of the function in the direction of the unit vector u = cos e i + si...

A: This question is based on del operator.

Q: Evaluate the integral and find a + ß+p-o (1+ tan x)dx cos? xV5 – 3 tan2 x va Sa 1 arcsin 1 tan x) + ...

A: Given

Q: Evaluate the integral. -2x dx 19 x e NOTE: Enter the exact answer.

A: Integrate it by parts. 

Q: 5. Discuss real world quantities that the circulation of a vector field around a closed loop could m...

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Q: Exercise 7. GREEN'S THEOREM Use Green's theorem to calculate fo F R. All curves are oriented counter...

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Q: Question Select your answer. On which interval(s) is ƒ(x) = 2 ln(x² +x – 20) continuous? (-00, –5) (...

A: Topic:- calculus  Note :- as per our guideline if more than one question uploaded than only first qu...

Q: lim +2-3t メー→3 十-3

A: Topic:- limits

Q: sec ~dx 3 In sec - + tan- +C 3 3 3 A True B False

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Q: Let F = (6e", 5 sin(x), 8 cos(x)). Calculate div(F) and curl(F). (Use symbolic notation and fraction...

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Q: Tutorial Exercise Evaluate the integral. dx Step 1 Recall the Inverse Substitution Rule, where f and...

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Q: У(x2 — у2 + 1)dх — x (х2—у2 — 1)dy %3D0 - -

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Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: What does the following equation represent in R? 7x - 6y = 0 Circle Line Plane None of the others Sp...

A: Topic:- geometry 

Q: x? 2. dx x? +9

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min....

A: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min....

Q: Calculate the divergence of the vector field F (x, y, z) = –10 sin(2xy)i – cos(x'y)j. (Give an exact...

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Q: -5 1 -2 0 3 4 12 -1 3 B| Find AB for : A = |1 B = 5 4

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Q: 2sin(e²^) cos(e²") dx, we let u=e2 To evaluate A) True B) False

A:

Q: To evaluate Je ?" sin(e²^) cos(e²«) dx, we let u=e A True B) False

A: Integration true or false

Q: Use Newton's method and find an approximation for the root of the following function accurate to wit...

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Q: 5 5 Find the result of this equation and put it in the blank a) lim f(x)

A: Right hand limit

Q: An airplane is flying on a horizontal path at a height of 3500 ft, as shown in the figure below. At ...

A: The solution of the problem is given in the next steps.

Q: -4 -4 At the point shown on the function above, which of the following is true? Of' 0 O f' > 0, f''...

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: Make a conjecture about the derivative by calculating the first few derivatives and observing the re...

A: Here, to make a conjecture about the derivative by calculating the first few derivatives. ddx(sin x)...

Q: 7 B lim f (x)% = 6 T--2- A 2 1(-0.1, 0.5) B2 -7 -6 -5 -3 +2 2 -1 -2 -3 F E 3.

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Q: range of the function. (a) If f(x) = 3x + 4, find the image of 4. (b) If f(x) = 7x + 5, find the ima...

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Q: For the function ?(?) = 1/4e^x+e^-x 1. Set up the integral for the length of the curve segment along...

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