using seperation of variable method, solve dy/dx=x3y2

Q: Use the First Derivative Test to find relative (local) maximum points points, if any, of the given f...

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Q: he given series converges or diverges. use the following as proof: rison Test, Integral Test, Series...

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Q: Check if the following is true or false: (x² + 3)dx = 18 %3D

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Q: dx - = In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+ 1)

A: Let's find. 

Q: Let {an}n=1 be a convergent sequence such that a1= V5 and an+1= 5an Compute lim an

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Q: 3. Find the arc length of y = 3x3/2 on the interval 1<x< 3 %3D

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Q: Find the derivative of the function. 3. 2x2 - 5 =イ 4- x %3| y' = ||

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Q: What are the radius and center of the circle that passes through the points (2,0), (18,0), and is ta...

A: From the equation of the tangent line we can deduce that the slope of the radical line would be -1/4

Q: [(2-sec²x) elnate sec³x dr What should be the value of A for to be integrable using the formula 'du ...

A: Let's find. 

Q: I. Solve the following: 1. Given: y 2x - Find: a.) dy/dx b.)y" 2. Given: 16y – 9x = 144, find y"

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Q: Evaluate * cos (e + a?) dx 24 +1

A: To find: The integral ∫44cose3x+x2x4+1dx Concept used: ∫aaf(x)dx=0

Q: Find the vector component of v = (4,–1, 7) along b = (1, 4, -8) and the vector component of v orthog...

A: Given: v=4,-1,7 &amp; b=1,4,-8   We know that; The expression for the vector projection v onto b is:...

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the c...

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Q: 5. y = xArctanx - In VI+x

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Q: The area of the region between the curves y = x2 and y = x from æ = 0 to x = 1 can be evaluated by |...

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Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate t...

A: a) summation of  n/(n3 + 1). b) summation of (n2 + 1)/(n3 + 1). c) summation of n3 / 5n.    

Q: dx For (x+x³)(x Tan-!x +1) = In[F(x)]+ C• What is f(/3) if C = 0? 3 V3 6 + 3 +

A: Given:     ∫dxx+x3xTan-1x+1=lnFx+C    =∫1x+x3xTan-1x+1dx substitute u=tan-1x →du=1x2+1dx     =∫cot2u...

Q: (14) = (x – y + 5)? dx dy %3D dy (15) (x² – y²)" – xy = 0 dx dy (16) 2xy = x² + 2y² %3D dx

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Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate t...

A: To check the convergence of the given series.

Q: Determine the values of a, b, and c such that the cubic function f(x)=ax^3+ bx^2+ cx satisfies all o...

A: Given problem:- Determine the values of a, b, and c such that the cubic function f(x)=ax3 + bx2 + cx...

Q: s, if any, of the given functions. De ion is increasing or decreasing. y = = x' - x

A: We will find the maximum and minimum value. 

Q: Question 1 2dy Evaluate the integral Зу — 4

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Q: I Find the second derivativety") of the following functions and simplify the final results. 1. y= x-...

A: Let's find. 

Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4.

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Q: Determine the convergence or divergence of the following series. 1 (a) Σ (Use Integral Test.) n(ln n...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 4. Ir log a 1, log, 81=b and log, 4 2 then find the value of log ().

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Q: Given a curve Determine the unit tangent vector, T, the principal unit normal vector, N and the bino...

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Q: 8969 2. find 121 detA)? OY

A: As per our guidelines we are suppose to solve only first question if the multiple questions are post...

Q: Find the area of the region bounded by the curve y=1. and the x-axis.

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Q: ACID MIXTURE: A chemist needs 10 liters of a 25% acid solution. The solution is to be mixed from thr...

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Q: C. Optimization 1. Use the first derivative test to determine the relative extrema of the following ...

A: The given function f(x)=x2x-22

Q: Let (P) be the surface given by the following equation + 4 and (Q) be a surface given by the below f...

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Q: J, sin a sin? cos" ,dx COS 2 2 2.

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Q: If Fx) is an antiderivative of x2 +x1, then what is the value of F(1) - F(-1)? 3

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A: Topic = Integration

Q: C b 630 A 53

A: Topic = Triangle

Q: Imagine that at a particular time, a kitchen counter has on it 10 bacteria and that this type of bac...

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Q: 9. Evaluate the definite integrals (give exact answers): a) (2x + 3)(r – 5)dx b) e -(1³ – 2x² + 1)dx

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

Q: I Find the second derivativety") of the following functions and simplify the final results. 1. y= x ...

A: Differentiate with respect to x. 

Q: 2. Find the vertical asymptote/s of 7.x f(r) : %3D x2 - 3r- 28'

A: Here we have to find the vertical asymptote of the function f(x)=7xx2-3x-28

Q: Find the three positive numbers whose product is 27 such that their sum is as small as possible.

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Q: Determine the following information regarding the function + 2(x - 4)- A. f (x) f "(x) Intervals of ...

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Q: 4. Find the area under the curve y = Vx +6 from x = -6 to x = 3. Give exact answer.

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Q: The population of treated mosquitoes comes in thousands, in a tropical rain forest at time m, in mon...

A: Given: For (A), Sketch:

Q: The range of the function f(x, y) = 16-4x-9y is equal to: [0, 16] [0, 16[ This option This option [0...

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Q: A pendulum consists of a 3.5 kg stone swinging on a 4.1 m string of negligible mass. The stone has a...

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Q: If f(x) = x + V2 – x and g(u) = u + v2 – u, is it true that f = g?

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Q: The antiderivative of ƒ (x), which is F (x), exhibits an odd symmetry, i.e., it satisfies the proper...

A: Given Problem is solved in attachment.

Q: CHAIN RULE DERIVATIVES glx) = (2 -7x)" %3D 2.) G) - 52 3) y- (6+5t-t) 4.),9(x) = (4u* – eu

A: As per guidelines we can solve only one question at a time so the derivative of first  question can ...