Зx* у + tan y dy Given a first order differential equation dx Q3 x' +xsec? (a) Clarify the exactness of the given differential equation.

Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: To differentiate.

Q: Problem No. 1: Evaluate - dx using basic substitution method.

A: First I have used the substitution to make integral easy and then evaluate it.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given:-the region bounded by x=y4,  x=1rotating about the line x=7using washer/disk…

Q: Find the exact values of the six trigonometric functions of each angle 0. (a) y (-V7, -1) sin(0) =…

A: (a) From the given figure: Here, OA=AB2+OB2=7+1=8=22

Q: xp - )s ɛ

A: As per the guidelines I can solve only first question

Q: Solve the following second order homogeneous linear differential equation if the 4 initial…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: х — у 3. f(x, y, z) = y? + z? а. f(3, –1, 2) b. с. d. f(2, 2, 100)

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Q: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

Q: Find r'(t). r(t) = (tan '(7t))i+t cos(t)j – /tk NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: 1 - dx = x² – 6x+8 -4 +C х-2 (A) In x- 2 In 2 (B) +C - 4 (C) 극미(x-2)(x-4)|+ (D) n|(x-4)(x+2)|+c (E)…

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Q: Let y=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

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Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 13 9ts r(t) = e"i+etj K(t) :

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Q: 1. Differentiate and simplify. a. .2 y = 3x+3x ||

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Q: Find the distance from A to C across the gorge illustrated in the figure. 130 ft The distance from A…

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Q: Solve the following problems. 1. (x²-2y²) dx+3xydy=0

A: This question can be solved using the concept of homogeneous differential equation.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given problem:- r(t)=cos(πt)i-ln(t)j+√(t-6)k ,t0 =7 find domain of r(t)and r(7)

Q: For x = t3 + 2, y = 3 – t, give an equation in terms of x and y.

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Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: We need to solve differentiation problem.

Q: Determine the vector field of F. F(x, y) = 6i – 3j

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Q: Evaluate the definite integral. 1+eJ+/k]di i-ej+ k o ? - 1 1 + (-" – 1) j + k e-1)1- (e - 1) J+ k o…

A: Given: I=∫01e9ti+e-tj+tkdt As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫eax+bdx=1aeax+b+C

Q: proportional

A: We will solve the problem.

Q: Evaluate the definite integral. e12' i + e¯*j+tk )dt e12 – 1 1 (e- – 1) + 12 O el2 – 1 e12 -i - (e-…

A: Integral

Q: Which substitution is needed to evaluate the integral S tan* x sec² x dx =? u = tan* x, du = sec? x…

A:

Q: Given z = f(а, у), а — г(и, v), у — у(и, v), with 2(0, 2) = 1 and y(0,2) 4, calculate z,u(0, 2) in…

A: We have to find the value of zu(0,2).

Q: Use Disk Method only Find the volume of the solid formed by revolving the region bounded by the…

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Q: 2. S CoSx+sinx-1

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Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: X+3 24) Find the integration by using: J: dx 2x3-8X

A:

Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…

A: Parametric plot÷

Q: 1 3. Savads 4Vūdu 4.

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Q: Select the best answer. (2e + 1)= lim (tan(x))- O DNE O -00

A: We have to find out limit

Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

A:

Q: dz dz and dy dx Suppose z is a function of x and y, and tan y² + x² = z®e6y. Solve for

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Q: Given the equation z + 10z°y – 8y² + z* = 4 az Use implicit differentiation to find dz

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Q: A. Identify the given differential equati. as to the dependent variable, degree of the equation,…

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Q: Find curl (8z i + 9x j + 10y k). curl(8z i + 9x j+ 10y k) Di +(i Dj +( )k

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Q: Use Disk Method only Find the volumes of the solids generated by revolving the regions bounded by…

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Q: 1. Let -1 -5] 3 -7 3 -6 -3 A = B= 6. 5 -3 -2 4 2 | -3 Determine which (if any) of the following…

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Q: Describe the graph of the equation. r = 14 sin 17t i – 14 cos 17t j O It is a circle of radius 14 in…

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Q: 3. S- dx 1-sin'x

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Q: Let T6 (x): be the Taylor polynomial of degree 6 of the function f(x) = cos(x) at a = 0. Suppose you…

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Q: Determine the largest interval that pλ must lie in to approximate p with a relative error of at most…

A: 3. Determine the largest interval that pλ must lie in to approximate p with a relative error of at…

Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…

A: To solve the given integral.

Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

Q: A famous leaning tower was originally 184.5 feet high. At a distance of 130 feet from the base of…

A: Using sine rule, all parameters are evaluated.

Q: dx ²+8x-9

A: Given: ∫dxx2+8x−9 Let I = ∫dxx2+8x−9 ⇒I = ∫dxx2+9x-x−9

Q: Find fr(x, y) and fy(x, y) given f(, y) = (csc y) Arcsin(x²). %3D

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Q: Find all points (if any) of vertical tangency for the curve represented by x = t? + 2t – 3 and y =…

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Q: 7. Given that tan (A) = and angle A is in 3rd quadrant and cos(B) = – - and %3D 13 angle B is in 2th…

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Q: 3 to dy 2 +Sinx COSX

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