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Q: Match the equation (written in terms of cylindrical or spherical coordinates)  = 5, with its graph.

A: Solution: Consider the general equation of the sphere is x-a2+y-b2+z-c2=r2 we have a relationship be...

Q: In Exercises 47-60, solve the initial value problem.

A:   In Exercises 47-60, solve the initial value problem.  

Q: EXAMPLE 2 Computing a volume Find the volume of the solid below the surface 1 f(x, y) = 2 + - and ab...

A: Given: fx,y=2+1yy=xy=8-xy=1  

Q: Let fbe the function defined by f (x) = ta Ifg (x) = f (7) and g (2) 1, what is the value of g (2)?

A: We have to use f(1) = 2.

Q: Arc length of polar curves Find the length of the following polar curves. The complete circle r = a ...

A: Given: The polar curve, r=asinθ, where a>0.

Q: Question 3

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Q: Evaluate the integral: ( ) sect tan ti +tcos 2t j+sin² 2t cos 2tk 1k)dt

A: the given integral is: ∫0π4sect tant i^ +t cos2t j^ +sin22t cos2t k^ dt we have to evaluate the give...

Q: Consider the line given as solutions to the equation 3x – 4y = 7. (a) What is the slope of this line...

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Q: f(x) = 2x - 3 a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate...

A: Given: f(x)=2x-3

Q: Find the Maclaurin series for f(x) = (1 + x)k and determine its radius of convergence. Assume that k...

A: We have given  fx=1+xk Then, by the definition of maclaurin series fx=∑n=0∞fn0xnn! fx=1+xkf'x=k1+xk-...

Q: Find the shaded green area y 20 19 cos(x) 01 19 sin(x) -10 20 Answer:

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Q: Determine the points of discontinuity. State the type of discontinuity ( removable, jump, infinite, ...

A: Given:  The function, g(t) = 1t2-1

Q: Evaluate the following limit, if it exist. Show your complete solution.  1. lim?→?2 sin2(2?)/1−sin2?...

A: To find the given limits.

Q: Find the derivative of the function.

A: Given- gx=∫1cosx1-t23dt To find- The derivative of the above function. Concept Used- Using the Labin...

Q: Manipulating Taylor series Use the Taylor series in Table 11.5 to find the first four nonzero terms ...

A: Given that, fx=xtan-1x2 And in table 11.5, tan-1x=x-x33+x55-x77+...            ...(1)

Q: Plot the point with the polar coordinates (3, 315°)

A: Here given polar coordinate asr, θ=3, 315° Here  θ=315°=315×π150=21π10 Therefore r, θ=3, 21π10  

Q: Explain how to find ∫ tan15 x dx without actually integrating.

A: ∫tan15x dx=∫tan13x tan2x dx=∫tan13x sec2x-1 dx   ∵sec2x-tan2x=1=∫tan13x sec2x-tan13x dx=∫tan13x sec2...

Q: Your firm has recently started to give economic advice your clients. Acting as a consultant you have...

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Q: I seem to be stuck on this and i have tried a lot of different approaches but in the end just confus...

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Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation, x+2y...

Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation ...

A: Consider the following equation: x2+y2-2z2=5                                             ...... 1 Cy...

Q: A boat is pulled in to a dock by a rope with one end attached to the front of the boat and the other...

A: According to the given information, Given that,    BC = 6 ft dydt=-0.6 ft/sec Because y is decreasi...

Q: Find the general solution of -3 y' = 2 -3 2 %3D у. 2 -3 2 2 ||

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Q: An equation of a quadratic function is given f(x) = -2x2 - 12x + 3. Solve; a. Determine, without gra...

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Q: For thousands of years, gold has been considered one of Earth’s most precious metals. One hundred pe...

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Q: 1. The beam AB suhjected to uniformly disteibuted loadi pe shown in the figure beion is fixed at end...

A: The uploaded question information is not visible. 

Q: Question 34

A: Just use a general method, compare with standard equation, find an integrating factor so that after ...

Q: 10 cm 10 cm A container has the shape of an open right eircular cone, as shown in the figure above, ...

A:

Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in...

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as y=e...

Q: Prove that

A: Given  The equation is ddx∫u(x)v(x)f(t) dt =fv(x)v'(x)-fu(x)u'(x)    Fundamental theorem of calculus...

Q: Simplify (assume that variables represent non negative real numbers) √10x . √8x

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Q: find the point in which the line meets the plane x = 2, y = 3 + 2t, z = -2 - 2t; 6x + 3y - 4z = -12

A: The equation of plane is 6x + 3y - 4z = -12. The coordinates of the line is x = 2, y = 3 + 2t, z = -...

Q: Verify identity (tan2 x - cot2 x)/(tan x + cot x )= tan x - cot x.

A: Given,                 tan2x-cot2xtan x+cot x=tan x - cot x To verify given identity we consider LHS...

Q: Fill in the blank/s : Using the definitions of six trigonometric functions, the trigonometric functi...

A: Given the fill in the blanks about the 6 trigonometric functions. We need to use the definitions of ...

Q: In the exercise 2x2 - 4xy + 5y2 - 36 = 0, Solve, If the graph of the equation is an ellipse, find th...

A: Given The equation of conics  is 2x2 - 4xy + 5y2 - 36 = 0 .

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 16y = 32t - 8 e -...

A:                                               Given: y'' -16y=32t-8e-4t   ;      y(0)=0;   y'(0)=15A...

Q: Evaluate the integrals in Exercises

A: Given integral is ∫0π2costi-sin2tj+sin2tkdt

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.