1. Determine the slope of the tangent line to the function f(x) = 2                                                                                                   x+1 at x = 5.

Q: y= 3x³etan ( – 4x)

A: Topic:-  derivatives 

Q: x^2=Axy+By

A: Simple value put

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y ...

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Q: Rewrite the integral in the 5 other orders. Explain your answers. 2 4-y2 f(x, y, z) dz dy dx

A: The given integral is ∫x=0x=1∫y=2xy=2∫z=0z=4-y2fx,y,z dzdydx. The domain of integral is R=x,y,z: 0≤x...

Q: Rewrite the equation as a quadratic in cos x, and then factor. 36-36 cos^2(x)=36-18 cos(x)

A: factors are:-

Q: 1. Prove that the two sets of conditions are equivalent. Here, T is a linear transformation and u, v...

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Q: Find the general solution to the differential equation. x' = t   4 + t x =

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Q: ах? + с, x < -2 a) Given f(x) = }bx + 8, - 2<x < 3, determine the values of a, b, and c if: -2c, x2 ...

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Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. cos'x sin x dy + (y cos>x – 1) dx = 0 2. xy' =2xex - ...

A: Given that: y.dx+x(lnx-lny-1)dy=0, when x=1, y=e

Q: Solve 3y fip %3D dr 2x

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Q: sin xcos* xdx х cos

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Q: Sx (x +1) /3 dx

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Q: [x sin(2x)dx

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Q: The transformation of a function f (x) into a function g(x) is given by g(x) = Af(Bx + H) + K. %3D w...

A: Topic = Functions

Q: ) Differentiate:  (a) f(x) = √x(cos)x2 (b) f(x) = 2x/x2 + 4

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Q: A company can sell x units of a product when the price is p = D(x) = 3.00 – 0.002x dollars. The tota...

A: Given , No of unit =x Price=p Also given P=D(x) =3.00-0.002x and C(x)=0.006x2+0.52x+270 Hence,    

Q: 6. The limit of that constant is that constant. 7. The limit of a constantc times a function is equa...

A: Since we are given with the multiple number of questions and our guideline is solve the problem only...

Q: The graph of f (x) is given by Determine the following limits. Write your answer in the form lim f(x...

A: Topic = Limits

Q: Given sets X and Y. For x EX and for y E Y, we form the Cartesian produc X x Y := {(x, y) : x E X, y...

A: Given that: X={-1, 1}Y={-2, 0, 2}

Q: 19. What are all values of x for which [ P dt is equal to 0 ? (A) -2 only (B) 0 only (C) 2 only (D) ...

A: We have to find the value of x. 

Q: Determine the general solutions of the following non homogenous linear equations. 1. (D² + D)y = sin...

A: As per the instruction, we will be answering the first one. For (1),         D2+Dy=sin x The charact...

Q: Use substitution to convert the integral to an integral of rational functions. Then use partial frac...

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Q: The height of a hot air balloon can be modeled by the function S(t) = −2t2 + 60t + 1, where S(t) is ...

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Q: f(x) =sin x. 1) find f'(x). Second, Third, and Fourth derivitive.   2) What is f^(4n)(x) when n i...

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Q: The transformation of a function f(x) into a function g(x) is given by g(æ) = Af(Bx + H) + %3D where...

A: We are asked to find the transformation.

Q: y" + 4y = 4 cos x + 3 sin x – 8

A: For particular integral of cos ax or sin ax we put       -a^2 in place of D^2 in F(D)

Q: The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his pioneeri...

A: Euler deduce that 12=1-1+1-1+1-1+......and-1=1+2+4+8+......by substituing x=-1 and x=2 in the formul...

Q: In 2004, an art collector paid $84,275,000 for a particular painting. The same painting sold for $27...

A: let the equation be V(t)=V0ektwhere  V0 be the initial painting valuet be the timek be the rateV be ...

Q: Southern Traditions sold the home decor division of their company 8 years ago and immediately invest...

A: Explained below 

Q: Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider...

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Q: If f(x) tan (5x), find f (x). Use exact values. f'(x) =

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not evalua...

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Q: (b) (x² + xy) = y² y = 1 when x = 2 dx dy (c) - y = e* sin(2x) y = 1 when x = 0 |

A: Given : (b)  x2+xy dydx=y2  ,         y = 1 when x = 2   which is y2=1 (c)   dydx-y= ex sin2x ,     ...

Q: Find the 1.crit numbers, 2.open intervals where the function is increasing and where the function is...

A: We need to find critical point and interval of increase and decrease. 

Q: Consider the series. (6)-()' - (3)'- (3)' -- + + This series can be written as a geometric series in...

A: Given that: 83+832+833+834+...

Q: ) Sketch the region enclosed by the given curves and find its area. y = -x² +4x, y=x² – 2x

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Q: Find all solutions of the equation in interval [0,2pi). 6sin^2(x) = 6+3cos(x)

A:

Q: 8. Calculate the unit rate. Over the weekend, Mr. Quinn burned some CDs with his favorite songs from...

A: Given Total song burner=275 Total number of CDs is used=25

Q: |sin² xcos“ xdx

A: The given integral is: I=∫sin2(x) cos4(x) dx

Q: Use the graph of f (x) = – below to find a number & such that f (x) – 0.25| < 0.1 whenever 0< |x – 4...

A: Here, f(x)=1x is the given function.

Q: 4. Given that aj = 3, ) ak = 1 and ) bk = 5, it follows that k=1 k=1 Eak and > 2ak + bk k=2 k=1 8. |...

A: Calculus   -  summation and  series 

Q: Evaluate the ff: 23 D S fda, given f 6)- and acx) F 1 3+3 X

A: Let's find. 

Q: Ay To the right is the graph of the greatest integer function, which is denoted by [x] and is define...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: 2. (D+7)°y = 0

A: Hope you are asking for question number 2 in part C  I am answering it here.

Q: Solve the Bernoulli Equation xyy' + y² = 2x

A:

Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where ...

A: Given graph:-         To find:- Transform f(x) into g(x) where the transformation is g(x) = 2  f(x)

Q: A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never res...

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Q: 91. Proof Prove that (cos 0)i + (sin 0)j is a unit vector for any value of 0.

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Q: Southern Traditions sold the home decor division of their company 8 years ago and immediately invest...

A: Topic =Algebra