2+ 1- 3,

Q: (a) Find the curl of the following vector: A =r cos e f-( (sin & cos @ (spherical) (b) Find the dive...

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Q: 6. An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of...

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Q: Identify the intervals of increase and decrease, local minima and maxima, intervals of concavity and...

A: First we find derivative of f(x) then find intervals of increasing and decreasing. 

Q: the cost to produce x units of wire is C=50x+400, while the revenue is R=70x. find all intervals whe...

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Q: For the equation 2°y"+y'+ Y = 0. 1 y = 0, (z-1) a) Both 0 and 1 are regular singular points O b) O i...

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Q: 3. Vsin x +1 cos.xdx

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Q: If f(x) = tan (3x), then f'(x) = (A) 12 tan (3x) sec?(3x) (B) 4 tan (3æ) sec2(3x) (C) 12 tan (3x) (D...

A: derivative

Q: Approximate the numerical value of f'(-1) using the graph provide 5 4 3+ 2- 1 54 3 -2 -1 23 4 5 -2- ...

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask th...

Q: The radius, r, of a sphere is increasing at a constant rate of 0.05 meters per second. a.) At the t...

A: Let  y=f(x)  be  the  given function. Then      f '(x)  is  the rate of change of f with respect to ...

Q: Suppose that Stuart is 6 feet tall and is walking towards a 20-foot streetlight at a rate of 4 feet ...

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Q: dy + ydx = 2xy² e*dx

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Q: az if If f(x) = then the if *<1 values of a and b such that f is differentiable on bx + 2 (-00, 0) (...

A: Topic = continuity and differentibility

Q: Solve for K- cooling Constant T(t)=T3+(To-Ts)ekt Ts e-kt=T(t)- To-Ts T(t) T(t)-Ts In e-kt=In- То-Ts ...

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Q: Example 7: Form the partial differential equation by eliminating the constants from 2= axe" +a* e +b...

A: In this question , we can form the partial differential equation by elimination the constants by usi...

Q: Determine the volume of the solid formed by revolving the area bounded by x = 4y-y and y=x about the...

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Q: what should x be to make the equation true? 2sinx=1 2sin2x=sqrt3 2sin3x=2

A: Topic = Trigonometric equation

Q: ax4 If f(x) = if x >1 then the if values of a and b such that f is differentiable on bx - 6 (-00, 00...

A: We will use derivative and continuity to find solution to the problem .

Q: Let W be the region that is cut aut from x't v<4 by the pora blae id Rs X'ty ond the plane =10. Eval...

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Q: Use the Extreme Value Theorem to show that the function f has both a maximum and a minimum value on ...

A: Given:      fx=9-2x2+x3 interval a,b=-1,1  Take derivative equal to zero to get critical points.    ...

Q: If f(x) = −2x^3 + 5 what is the average rate of change between x = −1 and x = 4

A: Use formula of avg rate of change

Q: Suppose the weight of a person was measured every five years according to the table shown. Determine...

A: topic - graphs weight of a person grows continuously . tangent line touches graph at one point and s...

Q: If f(x) = 4c0s(x) , then f'(x) = %3D (A) – sin(x) 4°os(x) (B) – In(4) sin(x) 4cos(x) (C) In(4) 4cos(...

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Q: Write the general solution of the given differential equation. y'' + 5y' + 6y = 6e^4x .

A: solution of differential equation

Q: 2" Determine the value of the series E or conclude that it diverges. n =0 102" + 1 Selected Answer: ...

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Q: Calculate the surface integral S FdS, where S is cylinder r² + y = 1, 0 + yz, 3 =

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Q: 4 (0) = 4l6)=3 Soluhon DE: Y= 64,-442

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Q: Q. 7 Use Newton's method to approximate the real root of the equation x- 3x + 3 = 0 up to four decim...

A: The given equation is: x5-3x+3=0 Let, f(x)=x5-3x+3⇒f'(x)=5x4-3&amp;f(0)=3f(-1)=-1+3+3=5f(-2)=-32+6+3...

Q: Determine the power series expansion (in sigma notation) of the function f(x) = sin 2 at x=0 A. Σ (...

A: Solution of the problem as follows

Q: Use the integral test to determine the series converges or diverges 5n Σ .2 n=1 n+5 Diverges Converg...

A: We need to find if series converge or diverge.

Q: Compute integrals b) dz 7 cos(z) ris Countercleckunse oriented rectangle with -2,ス-6,2tースォ Jis fount...

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Q: The graph of f(x) is shown. Which graph would best represent the graph of f (x)? 5 4 3-2 -1 1 2 3 4 ...

A: topic - functions and derivatives  if rate of change of function is constant number greater than zer...

Q: Determine the general solution of: y'' − 21y' + 110y = 10x.

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Q: Find the volume generated when the area bounded by the two curves of x2 = 4y and y2 = 4x is revolved...

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Q: If y" – 2y' + 3y = 0, y(0) = -2, y'(0) = 1, then L{y(t)} = Y(s) = a) 2s+3 82–2s+3 b) 2s+5 g2–2s+3 c)...

A: The given differential equation is y''-2y'+3y=0 ....................(1) Let y=emt ⇒y'=memtand y''=m2...

Q: Fld= is it conu or div

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Q: 3. Rewrite each of the following expressions in the specified form. Show the steps leading to your a...

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Q: If f(z) = 6tan(z) , then f'(r) = (A) In(6) 6tan(2) (B) sec2(z) 6tan(2) (C) In(6) sec2() 6tan(z) (D) ...

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Q: Find the curl of the following vector: sin e cos @ (spherical) (a) A =r cos 0 f-(no cos 2@ (spherica...

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Q: 18. Use limits to find the area between the graph of the function and the x axis given by the defini...

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Q: f(x): at x = 3 X-3 f(x) = at x = 0 f(x)%3D%x6 at x - 0

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Q: Find two numbers whose sum is 20 and whose product is a maximum A None of the given choices (B) 10 a...

A: To find the two numbers whose sum is 20 and whose product is a maximum.  

Q: d'y 2(x(+ ) %3D dx

A: We to solve the given differential equation

Q: The area on the first quadrant of the circle x^2 + y^2 = 36 is revolved about the line y + 10 = 0. W...

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Q: What is the area of the largest rectangle that can be inscribed in a semicircle of radius 10 cm? A 1...

A: It is required to find the maximum area of rectangle that can be inscribed inside a semicircle of ra...

Q: 4. Find the equation of the tangent line to the curve 2xy+r sin y = 27 at the point (1.%).

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Q: x² +1 Use the e-N definition to prove that lim = 1. x2 + x +1 1.

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Q: 2. Ý -8y=0

A: The above problem is solved.

Q: Let f(x) = 20 − 5x and g(x) = −0.2x + 4. Determine if f(x) is the inverse of g(x)

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Q: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)...

A: We have to find derivative of f(x).

Q: Determine whether the following series converge or diverge. (Give reasons for your answers) 1. En=2 ...

A: