Solve the following first order differential equations, clearly showing all calculation steps dy 2y+2 (i) dx x² dy (ii) X + 2y = x³ dx y² (iii) dx xy+x² ala

Q: Find the divergence of the following vector field: 0 O 2z O O F = (y, -x + z², 3x)

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Q: Evaluate the following integrals: dx dx a. S b. f √81+16x² √16x²-9 C. S dx 49-4x²

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Q: Determine the angle, to the nearest degree, between the vectors= (4,6,-2) and y = (1,8,2)

A: Solution is done in step 2

Q: Evaluate the integral In 23 In y s s ex+y dx dy.

A: Given: ∫1ln23∫0lnyex+ydxdy

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: Find the area of the region that is outside the cardioid r = 7(1 – sin ) and inside the circle r =…

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Q: Let f(x) = In(64x2 + 16x + 26). (If an answer does not exist, enter DNE.) (a) Find the interval(s)…

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Q: A boy is pushing a box with a force that can be described by the function: (x) = x³ — sin 2x + 1,…

A: The answer is given below using the formula:  W = ∫abF(x) dx where W is work done and F(x) is force…

Q: A sketch of the region enclosed by y = x and y = f Area of the region = fot 4.25 2²+1 follows.

A: Given: y=x and y=4.25xx2+1 First find the intersection point Thus, x= 4.25x1+x2 ⇒1+x2= 4.25⇒x=…

Q: 2 OM a) Find the area of the region b) Find the length of the curve c) Find the surface area generat…

A: A detailed solution is given below.

Q: numerate and explain each briefly the six guidelines in solving maxima/minima problems

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: A balloon is rising at a rate of 3 meters per second from a point on the ground 55 meters from an…

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Q: 3. State the slope of the tangent to y = ln (2x + 1) at x = 1 a) = b) = - In3 d) In3

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Q: Evaluate the following integrals: 1. f(cos x + csc² x)dx 2. f(tan x + sec² x) dx 3. (1+sec² x) dx…

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Q: [44 408]. -4 -18 Find the eigenvalues and eigenvectors for A = [64 The eigenvalue a + bi = has an…

A: Using Matrix operation

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 1) L-1…

A: Given problem:- Find  L-1[(-3s2 -12s-8)/(s+2)3]

Q: Let the closed interval [a, b] be the domain of function f. The domain of f(x - 3) is given by (A)…

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Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: Find the curl of the following vector field: F = (z, 2y, -3x)

A: Follow the procedure given below.

Q: Consider the vector-valued function R(t) = {{ (a) Find the domain of R. (b) Show that is continuous…

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Q: Given cos(8)= - 5 m<8<³ 2 for π<8<- then tan(0) =

A: We can find the answer as below.

Q: Evaluate the integral. (Use C for the constant of integration.) [(sec²(t) i + t(t² + 1)² ₁ + t²…

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Q: The improper integral .0 Xe-VX2+4 √x² + 4 dx ∞ converges to -e-² the above none of the choices…

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Q: 5 -5 g(x) dx

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Q: Q) find differential equation of the following equation 1) y' = y-x y+x

A: Solution of the above differential equation is

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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Q: A(3) = A(8) =

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Q: Calculate the integral approximation S6 for 0 -1 4-² dx.

A: In this question we have to find the Integration.

Q: n 2sin(x)=1, on the interval 10, 2π], what is the value of x?

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

Q: Calculate the volume of solid of revolution when the region bounded by y = sin 2x and x² - y2 = 0 is…

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Q: Evaluate the spherical coordinate integral. 1- cos 2 2π π SS S p²sin & dp do de 00 0

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: Evaluate the definite integral. 1 ex dx 0 1 + e²x JO

A: We will solve the definite integral.

Q: y = 2 sin (20+ 4π 3 ^

A: Given query is to find phase shift.

Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 47

A: I am attaching image so that you understand each and every step. Answer is 227π512 square unit

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

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Q: Find the general antiderivative of f (x) = O2 ln ln 2x + C 1 O + C - 2 ln 2x O-In In 2x + C 1 O + C…

A: The function is given by fx = 4xlnx2 To evaluate: The most general antiderivative of the function.

Q: M Wed May 25 ... 99% webassign.net A pencil cup with a capacity of 33 in.3 is to be constructed in…

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Q: The function f(x) = max x, searches for the maximum value between a number. Prove formally that the…

A: Given; f(x)=maxi .xi

Q: Step 1 of 2: Determine the intervals on which the function is concave upward and concave downward.…

A: We need to determine interval of concavity.

Q: Given the graph which consists of lines and a semicircle determine ₂ f(x) dx (4,2) 2 3 4 5 -1 -1…

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Q: The price per square foot in dollars of prime space in a big city from 2010 through 2015 is…

A: According to Bartleby guidelines I can only answer the first three questions given.

Q: Determine whether the improper integral is convergent or divergent. 33) S ∞ dx x2/5 0 A) Convergent…

A: We know that integration of xn   is xn+1/n+1.   Here i attached the solution of this question.

Q: H.W: Sketch the following functions 1. x² + y² = z + 1 2. x² + y² + 2y + 1+ 2+ z = 0 3. z² = x² -…

A: In these question , we can sketch the given function . Note : As per our Guidelines , we can solve…

Q: There are two extremely important sequences that we will discuss in this chapter: arithmetic…

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Q: The question is in the image attached

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Q: 18 1510 18 50 Change the Cartesian integral - Change the Cartesian integral into an equivalent polar…

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Q: ) Find the Taylor series for f(x) = ln x centered at 3. Show All Your Work.

A: We can solve this as follows:

Q: Evaluate the double integral over the given region R. xy² dA 2 X + 1 R xy² SS. dA= +1 R (Type an…

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Q: Using a particular trigonometric substitution 2 1 + x dx √3 +1-V 4 26 π - the above 1+ 13₁ 2 √1-x²…

A: To solve the given integral.