Replace the Cartesian equation with an equivalent polar equation. x² + y² = 100 Or-10 sin 0 Or- 10 cos 0 Or-100 Or-10 orr--10

Q: Use the formula k(t): 390 t¹1 k(t) (4 +225 +26) = ||r' (t) x r"(t)|| ||r' (t)||³ r(t) = t²i+t¹5j X…

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Domain -3 ≤ x ≤ 8 -5 ≤ x ≤ 5 -7 ≤…

A: We can find the domain of the equation as below.

Q: Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y =…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: a. (7+7i)(i + 1) UNA 7+7i i+1 C. (727°) (121°) e b.

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Q: Find the tangent line approximation 7 to the graph of f at the given point. Then complete the table.…

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Q: 3. x dy + 6y = 3xyi dx

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Q: our answers.

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Q: Find the length of the curve. (Hint: u-s

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Q: Solve the D.E ý - 25 +2y = 2 X73

A: Please read whole answer your doubt will be cleared.

Q: Let T: R³ → R³ be a linear transformation such that T(1, 0, 0) = (4, -1, 2), 7(0, 1, 0) = (1, 3,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: π/4 x² dx (x²+4)5/2 0 (Use trigonometric substitution)

A: Given integral I=∫0π4  x3(x2+4)52 dx

Q: Radius of Convergence of a Power Series. Determine the radius of convergence for the series (n!)²zn…

A: Use ratio test to check the radius of convergence .

Q: 5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

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Q: II. Find Do not simplify your answers. 1. log, (2x² + y) + tan(x − ³) = sin−¹(x² − 1) +

A: Given problem:-

Q: 4- Suppose that you can learn N(t)= 64t - t³ words of a new language after 1 hours of study time. a-…

A: We have to find the rate in words per hour.

Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

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Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

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Q: Find Duf at P. NOTE: Enter the exact answer. Duf = f(x, y) = sin(3x – 4y); P(4,3); u || 35 i I

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Q: d (h) (cot ¹(2)) = d (i)=(sec ¹(1))= = d (j) (csc-¹(2)) = dr 1 du 1+² dz 1 du I√²-1 dz 1 du I√²-1 dr

A: Given problem:-

Q: 6. y" - 4y' + 5y = 4e³t; y(0) = 2, y'(0) = 7

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Q: 2 fx-²dx

A: Follow next step

Q: lim (√²-x-√√² + x) H418

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Q: Find the arc length of the graph of r(t) = ev NOTE: Enter the exact answer. L = 451 e√²ti + e-√² +…

A: Here we have to find the arc length of the graph of r(t)=e√2ti+e-√2tj+2tk , 0<=t<=√2ln5.

Q: y"+9y=2e³x

A: Given; y''+9y=2e3x So, we can also write as; D2+9y=2e3x So, the auxiliary equation is; m2+9=0

Q: Integrating Factor by Inspection: 1. (2y3x)dx + xdy = 0

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Q: 17 Select the conic section represented by the equation. 4x 2 -y 2 + 24x + 4y + 28 = 0. circle…

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Q: Find the laplace transform of f(t)= t²e³t sin 4t OF (s) OF (s) = OF (s) = OF (s) = OF (s): - OF (s)…

A: This question is related to Laplace transform, we will solve it using given information.

Q: Find the volume of the shaded region when revolved about the indicated axis. Y A B D 493 392 334 234…

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Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: 2 x + لوا + sech (π) = cot(y) + log2 (tanh(x))

A: Given,            ex2+2y+sechπ=coty+log2tanhxTo find : Find dydx.

Q: 12. lim [ln(t) sin(t)] t→0+

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Q: Find the differential dy of the given function. sec² x dy Read It Need Help?

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Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

A: Given data÷

Q: Find the directional derivative of f(x, y) = direction of Q(2, —2). NOTE: Enter the exact answer.…

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Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why. a- Lim 4 c- lim…

A: See the details solution in below

Q: Find the limit. lim (ti - 3j+t² k) 1-7 lim (ti-3j+t² k) 1→7 = i + i j+ k

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Q: Solve the given differential equation. All solutions should be found. dy 3x = e +9y dx NOTE: Use c…

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Q: 3x

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Q: Q: Evaluat the integral. Q₁ is's ex dxdy 3y +²

A: Here we have to find the integral.

Q: 7 What is the probability of getting two heads and one tail when a coin is flipped three times?…

A: solving

Q: 11. ydx + x(x²y = 1)dy = 0 -

A: y dx+x3 y dy- x dy=0(y dx -x dy) +x3y dy =0(x dy-y dx)-x3y dy=0dividing by x2;(x dy-y dx)x2=xy dy…

Q: u be a differentiable function of du (a) (er) dr d du (b) = (6") = b. Inb dr dr 1 du (c) (In u) dx u…

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Q: 8 An acceleration function is expressed as a (s, v) = s²-. ' (v+1)³ determine displacement by…

A: a(s, v)=s2-8(v+1)3v(s)=∫0s a(s, v) dv      =∫0s s2-8(v+1)3 dv     =s2v0s -8 (v+1)-3+1-3+10s     =s2s…

Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: dw a) Find for the following function. dt w = 2ye* -In(z), x = ln(t2 + 1), y = cos(2t + 2), z = et…

A: If w=f(x,y,z) and x =g(t),y=h(t) , z=u(t) then,    dwdt =∂w∂x.dxdt+∂w∂y.dydt+∂w∂z.dzdt. Note : As…

Q: For the graph below, the concavity switches at x = +1.7 and 0 and there are critical points at x =…

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√√x-1 1. lim x-5 x² - 4x - 5 2x…

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