Evaluate the given integrals. Seš (6 – e) dx -1 3. es (6

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Q: Solve the differential equation by using integrating factors. xy' = 3y + x2 y(x) =

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Q: +00 Inn E(-1)" n2 n=2 divergent convergent

A: To solve the following problem

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Q: 5+x-1 dx x3+1 4.

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Q: Shaw Abooraically that Fand 6 ace.ivee F)=-3x2+5,X20 gW=D5-x 3. theN explain why a restriction was p...

A: if we have to find inverse of function then interchange the x to y and we get f-1x.if y=fxx→yx=fyy=f...

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A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)>03t2-60t>03t(t-20)>0

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Q: Given the function f(x) = x – 15x², find all x-values where f has an inflection point.

A: Solution is written in below steps.

Q: Solve this differential equation: 0.07y(200 – y) y(t) =

A: Given: Now,               y' =0.07y200-y⇒dy0.07y200-y=dx⇒dy-0.07yy-200=dx⇒114y+-114y-200dy=dx⇒114y-...

Q: Let f be a differentiable function such that f(+5) =-9 and f'(x) = 2x + 8. What is the approximation...

A: Given query is to find the value of f(-4.9).

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A: This is a problem related to simple interest calculation. Based on the general formula of simple int...

Q: O Watch help video A particle moves along the x-axis so that at time t 20 its velocity is given by v...

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Q: Solve the differential equation by using integrating factors. xy' = 3y − 8x2 y(x) =

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Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: Question Find an algebraic expression equal to cos (csc- (3x - 3)). (You may assume that-< csc- (3x ...

A: Let's find. 

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Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t)= t° – t² - 5t. D...

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Q: Question 1 Find the derivative of g(x) = 3 cos™' (x) at the point x = 4 %3D %3D (Enter an exact answ...

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Q: -32 %3D Find the gradient Vf (x, y,z) OF f (x,y.z) = e sin 3X cos 3y

A: The given function,      fx,y,z=e-3z sin 3x cos 3y

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A: We need to find volume.

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A: We have to find ∫410f(x)dx  

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Q: x3dx 3. S (x4+4 )4

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Q: +00 El-1)nInn- n=2 n2

A: The given series,        ∑n=2+∞-1nln nn2

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Q: From Rogawski ET 2e section 8.1, exercise 9. Calculate the arc length of y = - x - In x over the int...

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Q: tf(r.,2) 4ry t and u is the unit vector in the direction of (4, 2,-5), tmen the drectional denvative...

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Q: Question 3 If f(x)=cos x, then f"(x)= O cos X

A: f(x)=cosx,f'(x)=ddxcosx=-sinxf''(x)=ddx-sinx          =-ddxsinx          =-cosx  

Q: a) Show that f(x) = |5x+6| is continuous everywhere. (One point in particular is important to check)...

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Q: If x? + y? = 100 and dy 8, find dt dx when y = 6. (Enter your answers as a comma-separated list.) dt...

A: Given that x2+y2=100dydt=8To find :dxdt when y=6Solution:x2+y2=100x=100-62=8x2+y2=100Diffranciate w....

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A: Given region bounded by y= sinx  from x=0 to x=1.4 

Q: (a) f(x) = (3x² – 1)/T +x/4 (b) y(x) = r-1 r³+2 (c) g(t) = [(t³ + 4)(t² – 1)]/

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Q: 3. (a) Suppose y is a differentiable function of r and is implicitly defined by the equation [(2r+1)...

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Q: 1. Evaluate the integral JS aA, where R is the region: {(x,y)|0 < x < 1, –3 < y< 3] x²+1

A: To evaluate the integral: ∫∫Rxy2x2+1dA where R is the region (x,y)|0≤x≤1,-3≤y≤3.

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Q: Sketch at least TWO PERIODS of this scenario on a graph. You can copy the graph below on a separate ...

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Q: 6 The points P and Q have position vectors, relative to the origin O, given by OP = 7i + 7j – 5k and...

A: (i) Given that: OP→=7i+7j-5k and OQ→=-5i+j+k. It means: P=7,7,-5 and Q=-5,1,1. The midpoint of PQ is...

Q: b. (2,1)

A: