Given s(t)=31²+12t, where s(t) is in feet and t is in seconds, find each of the following. a) v(t) b) a(l) c) The velocity and acceleration when t=2 sec

Q: ام 1. ( - 3x2 + 5x - 7)dx

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Q: COS X 6. y = x What is the appropriate formula? dx Solution:

A: Given query is to find the derivative of the expression.

Q: Find the future value of a $20, 000 annual income stream if it is invested immediately as it is…

A: Hee, use the formula: FV=erM∫0MS(t) e-rt dt

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

A:

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: to express the integrals as limits of [ f(x) dx (b) [f(x) dx

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Q: owin - y" −4y' +4y=0 L".

A: 1)  y''-4y'+4y=0 Auxillary equation is m2-4m+4=0m2-2m-2m+4=0m(m-2)-2(m-2)=0(m-2)2=0 ⇒m=2,2

Q: Write an equation of the form y=a sin bx or y= a cos bx to describe the graph below. ਨੀਲੀ 27 π 70 21…

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Q: Evaluate the iterated integral. 6 (x + y) dy dx Jo Jo

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Q: Evaluate the following 1. S sin x sin (cos x) dx

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Q: 1 A tank with a capacity of 400 gal initially contains 100 gal of water with 50 lb of salt dissolved…

A: 100gal=Initial amount of water in 400gal tank50lb=Initial amount of salt in the tank1lbgal=salt…

Q: √81 - y² ST (x + y) dx dy

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Q: 2. Evaluate each of the following limits using the function f(x), defined below. If the limit does…

A: The given function is: f(x)=x+3x2+5x+6

Q: ["u pus C=P Op2-13 an=19 +

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Q: 7.3 = x + 2y x-2y y'

A: This question can be solved using the concept of differentiation.

Q: Find the present value of a $45, 000 annual income stream if it is invested immediately as it is…

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Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A: Given;  Rope length =20m Height =8.2m

Q: Use the formula k(t) = = k(t) = ||r' (t) x r"(t)|| (t)||³ ||r' r(t) = t²i+t⁹j = to find k(t).

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Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: h(x) = f(gx)) calculate the following derivatives using the table a) h'(3) b) h'(2)

A: Given

Q: Evaluate the iterated integral. 6 [[° (x + y) dy dx

A:

Q: Find the total length of the curve r = acos² 0. (A) 3.12a B) 6.89a 1.19a 5.52a

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Q: y=x√3-2x³

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Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…

Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: 1 - √xdx

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Q: ANSWER

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Q: Consider the equation (a-y-2)dx + (x + y - 4)dy = 0. (a) Make a transform to reduce the equation to…

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Q: Evaluate the following integrals. 2. √x*+5x³ x+5x³+20x+16 x(x²+4)² dx

A: The given integral is ∫x4+5x3+20x+16x(x2+4)2…

Q: Plot y = B sin(Aπx) cos(x) with a solid line over the interval 0 < x < 3 with the vertical axis set…

A: close allclear allformatclc A = 21;B = 5;C = 3;y1 = @(x) B * sin(A*pi*x) .* cos(x);y2 = @(x) B *…

Q: Evaluate the iterated integral. [²] (x² - y²) dy dx

A: Given: I=∫-11∫-44x2-y2dydx   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: (a) f(x) = 2x³ + 3x² - 12

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

Q: [18x² √6x³ +5 dx 3 ○a. — (6׳ +5)³/4 + C b. (6x³ +54/5 + Oc.5(6x³+5)¹/5 + C d. 5 Od (6x³+5) ³/4 + C…

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Q: Use the One-to-One Property to solve the equation for x. - 2x 7 = 4 X =

A: we have to slove the above question and find the value of x

Q: 4 3 2 +..

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Q: 2. Let f be the function from {a, b, c, d, e} to {1,2,3,4} with f(a) = 3, f(b) = 1, f(c) = 2, f(d) =…

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it…

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Q: Find f''(x). 5 f(x) = (x² + 5) *

A: The given function,  f(x)=x2+55

Q: dy e2y-1

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Q: Find the laplace transform of ƒ (t) = 2t² + 4t – 5 OF (s) = 5s5+484+4s³ 86 OF (s) -58²-4s+4 83 OF…

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Q: y = 3x-2\4 4x-5

A: WE use the properties of logarithm to find the derivative

Q: The radius of the base of a cone is 6 inches. The slant height of the cone is 10 inches. Which is…

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Q: If f(x) = sinx and g(x) = cosx, then what is the relation between g'(x) and f""(x)?

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Q: Determine the equation of the tangent line to the function f(x) = x square root (5-x^2) at x = 1

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Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

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Q: Evaluate the iterated integral. 16-y² ST Jo (x + y) dx dy

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Q: . Given the fx²dx, which of the following is the integrand? C. x² A. 0 B. 2 D. dx

A: To determine what is integrand.

Q: Q/ By uesing chain rule Find du de For this functions E² +1 x² + y² X x = tanzt, y = e 2x a = / 11 ?

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Q: 1. find dy/dx of each equation using implicit differentiation. a. x2 - y2 = 9 b. 3x2 - y3 -3xy = 0

A: As we know that; The Power law; ddxxn=nxn-1 The Product rule; f·g'=f'·g+f·g'   Given: (a). x2-y2=9