I. Find dy/dx of the following: 4. y=√1+In²x 7. y In- COS X √4-3x² 5. y = sin²(In x) 8. y In, x- 6. y=In(In x) 9. y + ln xy = 1

Q: Find the particular solution of the differential equation satisfying the initial condition y(0) = 6.…

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Q: 4. Find the range of the function F(x)=√36-t² dt O [0, 36π] O [0, 18π] O [-6, 6] O [-6, 0]

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Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

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A: We can find the limit in the following steps.

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A: We have to find the equation of tangent line.

Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

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A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Given: R(t) = ti + t2j + t3k, find the curvature and the radius of curvature at any point.

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Q: 2) The region in the first quadrant bounded by y = x y = 2. Calculate the volume using the shell's…

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Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: Simplify. (2u²vw4)² 4(uw³)2

A: In this question, we need to simplify the given expression.

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Q: Solve the separable differential equation dx 2 dt and find the particular solution satisfying the…

A: Please see the below picture for detailed solution.

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A: Given problem:- 1+x2y'+2xy=11+x2y

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Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

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A: Given,            ∫14+x2dx

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Q: Question 7 (1 point) ✓ Saved The point (1, 2, 4) is on the line 2+³ = 1+4 = 25 True False

A: We have given equation of the line x+35=y+44=z+53 Put x=1,y=2,z=4 1+35=45 Similarly, 2+44=64=32…

Q: -5 -4 -3 -2 -1 5 4 3+ 2+ 1+ -2- -3+ -4 -5+ ܐ 2 3 4 5

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Q: 1) Think of a multivariable function that might model something in your own work, hobbies, family,…

A: Consider the temperature in a room, T=Tx,y,z which depends on the position of the point in a room,…

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A: The given integral is fx=4x9+4x7-4x3-8 Integration formulas: ∫xndx=xn+1n+1+C∫dx=x+C

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A: A television camera at ground level is 2000 feet away from the launching pad of a space rocket is…

Q: QUESTION 10 Use cylindrical coordinates to evaluate the integral below. √x² + y²dv, where E is the…

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Q: Find the limit of the transcendental function. (If an answer does not exist, enter DNE.) 6-6e-x lim…

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Q: R If is in standard position and ≤0≤ and sin 2 O 5 O_3 3 3 9 then the value of tan is:

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Q: annat pe 4 panda 40 god = mode O xp (9 − xx + ₂x) J rester auf dienser og ressatur aut to conflittop…

A: ∫24x2+3x-6dx=∫24x2dx+3∫24xdx-6∫24dx

Q: = { x + 15 X C(x) = if x < 100 if x ≥ 100

A: Topic:- function

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A: Here is the solution:

Q: Determine the following limit in simplest form. If the limit is infinite, state that the limit does…

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Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: 5-4-3 2-1 10 9 8 7 6 5 1 y 4 32 3+ 2+ 1 2 234 3 4 5 -6 1 2 3 4 5 X

A: Please see the below picture for detailed solution.

Q: intervals

A: A function is increasing if when y is increasing with respect to x ot vice versa. Hence, Given…

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Q: A manufacturer can produce 4320 cell phones when a dollars is spent on labor and y dollars is spent…

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Q: 13. What is the maximum value of the parabola ? 5 0 5 a) y = 3 b) x = 4.9 -Cr- 5 c) y = -1 d) There…

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Q: Express a = the limit lim Σ(4(x*)² – 3(x* )³) Aï; over [6, 7] as an integral. n→∞ i=1 Provide a, b…

A: The given limit limn→∞∑i=1∞4xi*2-3xi*3∆xi over the interval 6,7

Q: Suppose p′(−1)=−2 and q′(−1)=−5.5.  If r(x)=−7p(x)+10q(x), find r′(−1).

A: We have to find the value of r'(-1).

Q: The volume of a right circular cone of radius x and height y is given by V = volume of the cone is…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

A: The curve y=4x-6, for 52≤x≤92 rotated about y-axis we have to find the surface area of the solid