Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

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Q: dy = 3y + 2t dt %3D Given the above differential equation with the initial condition y(t=D0) = 5.0 a...

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Q: Problem Solving 1. Determine f(x) given that f'(x) = t* – t3 + t² +t – 1

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: Find the function M(r, y) such that M(x,0) = e- and the differential equation M(x, y)dx + (sin a cos...

A: Use the concept of exact form of the differential equation. 

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an...

A: The x-intercept is where a graph crosses the x-axis and the y-intercept is where a graph crosses the...

Q: Given F(2) = 5, F'(2) = 1, F(3) 4, F'(3) = 4 and G(3) = 2, G' (3) = 2, G(4) = 6, G'(4) = 4, find eac...

A: Given that,F2=5, F'2=1, F3=4, F'3=4G3=2, G'3=2, G4=6, G'4=4

Q: A potato is launched vertically upward with an initial velocity of 129 ft/s from a potato gun at the...

A: Rate of change of displacement is called velocity and rate of change of velocity is called accelerat...

Q: Find all the real-number roots of the equation. Give an exact expression for the root and also a cal...

A: solution:-ex-e-x-1=0ex-1ex-1=0ex2-ex-1=0using quadratic formulaax2+bx+c=0x=-b±b2-4ac2aex=--1±-12-41-...

Q: The curve -4x – 3y³ – 7x + 5y = 2 is shown in the graph below in blue. Use the graph below to draw l...

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Q: C. How long is the ball in the air? i. Describe how you read that off the graph ii. Describe how you...

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Q: Find 2- ベ-3 2メ-3 2X+3 X+4

A: Please refer to the image below

Q: Find the derivative of y Cos3 3x+8 (x). %3D Provide your answer below: y = D

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Q: Solve 2log (x+ 1) =log (x) + log (x+3). Don't forget to check for extraneous solutions.

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Q: 2. Let C be the graph of the equation In(3y – 2e*) = sinh (Tx) – tan(y – 1) dy (a) Find dx (b) Find ...

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Q: Let f(1) = (1 + 2x + 2)*

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Q: Suppose that f(1) = (2x – 5)°(5z' + 1). Find f'(x), and then evaluate f' atr= 2 and I = 2. f'(2) = f...

A: For the given function we find the Differentiation using multiplication rule as follows  -       If ...

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Q: Consider the following tables: -2 -1 1 2 f (x) 5 -3 4 3 -2 -1 1 g (x) 5 1 3 Fill in the blanks with ...

A: Function values of f and g are given, we have to find the following.

Q: Find the tangent plane to the surface at the given point. 2x+ 3y z= at P (2, – 1, 1) x+y

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Q: 2х + 6, х 6 From the following results, determine whether the function f(x) = is continuous at x = ...

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Q: Find f. f '''(x) = cos(x), f(0) = 9, f '(0) = 8, f ''(0) = 5

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Q: For the demand function q =D(x) = 100 find the following a) The elasticity b) The elasticity at x 7,...

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Q: Show directly that the given functions are linearly dependent on the real line. That is, find a nont...

A: Given: f(x)=17. g(x)=6sin 2x h(x)=3cos²x

Q: (a) Let f(x) = tanx- 2, g(x) = x5 + x³ and h(x) = Vcsc5x. Then find %3D the f(g(h(x))), using chain ...

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Q: Approximating Function Values In Exercises 43-46, use differentials to approximate the value of the ...

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Q: A box is partially filled with liquid. The length of the box is 18 inches. The width of the box is 1...

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Q: d²y Find dx2 if –10x – 6y = -6.

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Q: Book Design A book designer has decided that the pages of a book should have 1 in. margins at the to...

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Q: A nonhomogeneous differential equation, a complementary solution yc, and a particular solution y, ar...

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1 + 3y2,   ...

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Q: x +3, (x + 3)² 1+ + 22 32

A: This is a problem of series and sum calculation. First we will convert the given series into sigma f...

Q: f (x,y) =x³ cos y Given df (2, 1) дх of and (2, л). Evaluate ду

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Q: y³dy Let y = 2 sin 0 %3D 4- y2

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Q: Evaluate the integral. HINT: [Use a shortcut.] '5 3x dx x2 + 4

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

A: Find your answer below 

Q: For the following series, test for convergence by the ratio test. 1 1 (-1)"n + (-1)"-1(n + 1) - ... ...

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Q: ow directly that the given functions are linearly dependent on the real line. That is, find a nontri...

A: Topic:- algebra

Q: Evaluate the integral of the following transcendental functions. dy 4) [- V9-49y² x² – 4 dx 5) [ x² ...

A: Topic:- application of integration Note :- as per our guideline if more than three subparts posted t...

Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at x = 4. %3D (Enter an ...

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Q: Find h'(-2) if h= fog. f(z) = 372 + 8 and the equation of the tangent line of g at-2 is y= 4x 6.

A: Here we have to find h'(-2) if h=f∘g , g(x) =3x2+8 and the equation of the tangent line of g at -2 i...

Q: Here is the problem : a) Classify this differential equation as separable, linear, exact, or non-e...

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Q: Find the Wronskian of the functions f(t) = 2et sin(t) and g(t) = e' cos(t). NOTE: Your answer must b...

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