Given: x'(t) + 2y(t) = - 1 where, x(0) = y(0) = 0 x(t) - y'(t) = 2t Find : v(s) = L{y} 3 s(s² +2) s(s² +2) 1 s(s2 +2) 1 s(s²+2) S 3.

Q: Use numerical or graphical evidence to determine the left and right hand limits of the function. |4 ...

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Q: )1–2و( 24s (s²+1)* If the Laplace Transform of F (t) t³ sin(t) is f (s) = what is the Laplace Transf...

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Q: Identify the graph corresponding to the following function (t 0): y =tu (t – 1) – tu (t - 3)

A: solution is given below

Q: Let f(x) = x^2 −x −2. Using the Intermediate Value Theorem, explain why this function has (at least)...

A: The function is  f(x)=x2-x-2

Q: Solve [y (In x – In y) + x] dx +a (In y – In a) dy = 0 xlny + yln x = Cx None of the choices ylnx + ...

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Q: Find L{(1 – t) (3 + 2 sin 5t)} . 3 2s 10s - 82+25 (s2 –25)² - 10 20s 을 + - - s2+25 (s² +25)² 3 3 10 ...

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Q: TAT So use the 1. Show csC x =- CSC X Cot x. (Hint: csC X = quotient rule.)

A: topic - derivative of a trigonometric function note: as per bartleby guidelines, we are supposed to ...

Q: Consider the function 7 f(x) = 2 2 - - 5 -1<<3 3.x-17 3 < z<∞ Graph the function and use the graph t...

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Q: 5 1 from y = 1 to y= 2. 3 12y Find the length of the curve x =

A: NOTE: Refresh your page if you can't see any equations. . for simplicity interchange the variables

Q: Given the differential equation: y"+3y'- 4y = e42 Propose an appropriate particular solution Yp = (A...

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Q: Evaluate the limit, if it exists. If a limit does not exist, type "DNE". V4 + h - 2 lim h>0

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Q: Find the area of the shaded region. 15 ft 10 ft ft

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Q: Given the function f(x) = - 2x

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Q: 3) The magnitude of a velocity vector is speed. Suppose that a wind is blowing from the direction N4...

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Q: -0.5z 6 if a 2 -7- 6- 4- -8 -7 -6 -5 -4 -3 -2 2. -2- -3- -4 -5- -0- -7- -8+ Clear All Draw: 1. 50

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Q: 9.

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Q: A small metal bar, whose initial temperature is 40°C, is dropped into a container of boiling water w...

A: Follow the procedure given below.

Q: Answer the following True or False: For any function f(x) that is differentiable at z = 9. f( – 9 + ...

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Q: evaluate the integral of " [(x^2)+1] / [(3x+1)^0.5] "

A: The given integral,        ∫x2+13x+1dx

Q: Show that (4, 5) is on the graph of f(x) = 2x + 1. Since f(4) = 5 the point (4, 5) is on f(x). %3D F...

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Q: Evaluate f (2x + 1) dx by two methods: (a) Expand (2.x +.1)' by the binomial theorem; (b) let u = 2x...

A: Given that ∫2x+13dxa. using binomial expantion2x+13=c302x3+c312x21+c322x112+c3313=8x3+34x2+32x+1=8x3...

Q: 1 th X +7 Fy =

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Q: 0 2 4 6 8 10 12 f(x) =|-16-12 -10 -8 -7 -8 -10 . Estimate f'(2) using the values of f in the table. ...

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Q: For the function g(x) = - (x+4)2 +9, find each of the following by referring to the graph. (A) Inter...

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Q: the exact value of each trigonometric function  9. tan -30 degrees  15. tan 90 degrees  17. Sin 9...

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Q: (V- 1)2 Evaluate dx by two methods: (a) Expand (Vx 1) and multiply the result by x-1/2: (b) let u = ...

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Q: use trig substitution to evaluate the integral of "sqrt(16-x^2)"

A: Given problem:- use trigonometry substitution to evaluate the integral of "sqrt(16-x^2)"

Q: 7) cos 330°

A: "Since you have asked multiple question, we will solve the first question for you. If you want any s...

Q: Find the most general antiderivative of f(t) = 1 cos(t) – 5 sin(t). Note: Any arbitrary constants us...

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Q: О 10 O 5

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Q: 31) Find tue derivetive of tue funcrion heae) = I Sinh 2x -7X 4

A: For derivatives we just apply differentiation both side. 

Q: e2x +2e* -dx e* +1 2.

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Q: For the integral dr Vx+4 (a) Find the average value of f on [0, 5]. (b) Find a number z that satisfi...

A: Given: - The integral is, ∫051x+4dx (a) To find: - The average value of f on 0,5

Q: 16 Find F(0) if F (t) = L-} O 4 O 2 O 16

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Q: Use the graph of f and g. P(x) = f(x)g(x) %3D f(x) 9(x) = g(x) %3D 107

A: NOTE: Refresh your page if you can't see any equations. . take derivative take x=5

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,...

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Q: Use the limit definition of the derivative to find the instantaneous rate of change c f(x) = 4x + 7x...

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

Q: Find the angle e between the vectors in radians and in degrees. u = 6i + 3j + k v = 3i – 6j

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Q: 15 51 :- -/- -1- :- ーによ -1- イーキーーュ ナー ートー- ー ーー III II III IL 1,0 15 15 -1 ーャー- -15 r2 + 13x + 42 f(...

A: The given question can be solved as shown in step2.

Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +...

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by: a(x...

Q: A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for each gal...

A: Given:   A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for...

Q: Marginal Revenue for Producing Loudspeakers The management of Acrosonic plans to market the ElectroS...

A: Given:- Marginal Revenue for Producing Loudspeakers The management of Acrosonic plans to market the ...

Q: Let f(x) = the following transformation of the graph of f: horizontally scaled by a Vx. Find the equ...

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Q: Identify the graph corresponding to the following function (t > 0): y = tu (t – 1) - tu (t – 3) 1 + ...

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Q: A 2-lb-per-gallon salt solution is pumped in a 400-gallon tank at a rate of 2 gallons per minute. At...

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Q: Which of the following is equivalent to the differential operator (D-9)(D+9)y? O (D² – 2D+ 81) y O (...

A: To determine:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32 ft/...

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

Q: Find the volume of the solid formed by rotating the region bounded by the curve y = Va and the line ...

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Q: d Use the table below to find [1.3g(x) dx x= 1 1 3 4 5 f'(x) g'(x) 1 3 2 4 3 2 5 1 4 d [1.3g(x)] dx ...

A: Simply differentiate and put all the values.

Q: 3 5/3 3 1/3 + 6 for 13x<27. Find the length of the curve y = =x 4 5

A: We have to find the length of curve.