Water is pouring into a swimming pool. After t hours, there are 2t – vt gallons in the pool. At what rate is the water pouring into the pool when t = 9 hours?

Q: find the derivatives of the following with complete solution a. y = sec 2x b. y = sin x -

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Q: dx kx, x(t,)=x, dt where k is a constant of proportionality, serves as a model for diverse phenomena…

A: Topic:- function

Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: ydy J-7-By-y

A: Given problem:- ∫ ydy/√(-7-8y-y2)

Q: х3—х+1 Find: lim X→0 x2+3

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Q: 16. For the function g(x) = x² + x – 1, find and simplify: 9*+h)-g(x) h

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Q: 19. For the following function f (x) 3x-4 %3D find any x-intercepts, y-intercepts, and equations of…

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Q: Evaluate the limit, using L'Hôpital's Rule If necessary. (If you need to use or-w, enter INFINIT x -…

A: we have to find the limit

Q: Find the critical points of the function x -8x2 О 0,2, -2 O 0, 1 О 1,2, 3 this function does not…

A: Solution: Let f(x) = x4 - 8x2 find where f'(x) is equal to zero or undefined  f'(x) = 4x3 - 16x

Q: 1. Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. On…

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Q: 7. Particular solution of (D³ + 12 D2 + 36 D)y = 0, when x = 0, y = 0, y' = 1, y" = -7

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Q: The position of a particle in meters at time, t, seconds is given by s(t) = cos2(3t). Find the…

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Q: ACTIVITY 1: Determine if the following functions are continuous at the given value of x. If the…

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Q: Find the FIFTH DERIVATIVE Given: f (t)

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Q: V1-x² 1–x2 dy dx -1 . J-V1-x²

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Q: Find the enclosed area by the curve with equation f (x) = x² – 4 and g (x) = 8 – 2x2 40 35 36 32

A: To find the enclosed area between given two curves.

Q: 9. A boat floating in the sea rises and falls with the waves. A sailor on the boat will also rise…

A: Given, f(t)=12sin(pi×t/4) +8 where t is the time measured in seconds f(t) is the tailor's altitude…

Q: Area under the curve xy = -1 from x=1 to x=2

A: topic - area under the curve

Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

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Q: What is the exact value of csc(– 1305°)? V3 A B D 2.

A: using csc(-x)=-csc(x) and  csc(360n+x)=csc(x)

Q: ) Estimate the value of Csc (0. 2) using linear approximation and without using any kind of…

A: Given problem:- Estimate the value of csc(0.2) using linear approximation

Q: A particle moves along a straight line with its position given by s(t) = -5t2 + 7t + 2. Find its…

A: In this question, we want to find the average velocity between t=1 and t=3.

Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: C. Find y" for the following functions a. y-3y-x = 0 b. x + 4y2 = 12 C xy COs y

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Q: 18. Convert 5 radians into degrees. First find the exact answer (no decimals or rounding, please).…

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Q: ri rV1-x² dy dx -1 Jo

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Q: (3x-2) dx x²+ 2x + 15

A: the given problem is solved below in detail.

Q: a. You are about to eat a slice of pizza and decide to do a little PreCalculus first. The entire…

A: Let's find volume of slice of pizza.

Q: Find an equation of the tangent line to the curve y= x3 – 3x2 + 5x that has the least slope.

A: Given    slope is 1st derivative

Q: II. Evaluate each of the following limits. 1-V3-x 4) lim x→2 4-x2 5) lim x→∞ 3 Sin ) 2 6) lim(4x +…

A: We have to evaluate the given limit.

Q: Sove a lake, sere hft) represents the height above the water, in feet, at t seconds. a) Determine…

A: Topic:- application of derivatives

Q: Evaluate the following limit. 9. 5 +h lim h 0 Rewrite the given limit in a way that can be evaluated…

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Q: Evaluate the limit, using L'Hopital's Rule if necessary. In x lim

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Q: 4. (a) (i) Calculate (4 + 10i)?. Answer:

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Q: r(t) = (cos t)i + ( sin t)j + ( sin 6t)k, t, == (Type an exact answer, using radicals as needed..)…

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Q: -4x Calculate the following integral Je dæ by using a substitution O - 0.25e^(-4x) + C O 0.25…

A: ∫ e-4xdx

Q: (x+1 0SxS2 f(x) = { Then what is the result of| ($2) dz 5

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Q: 4. General solution of (y2 + xy) dx – x² dy = 0 %3D

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Q: 1 -2 Inx x-1 11. lim,» x→1

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Q: -2 Find f'(x). Given: f (x) = (2x3+3x2-5)2

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Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hopital's Rule. sin(9x) lim 7x…

A: We have to find the limit

Q: 3. Find the reference angle (also called the reference number) for the angle: 13n radians. 11

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Q: 2. By integration, show that the area of a circle of radius r is A = rr?

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: - The price-supply and price-demand equations of a certain product are given by p = S(x) = 15+ 0.1x…

A: To find the producer surplus.

Q: If f(x) = 5x² In(6x), then f'(x) = f''(x) = f'''(x) f(4) (x) = f (5) (x)

A: We have to find derivative of give function.

Q: Find the equation for the plane through the points Po(-5, - 2,- 2), Qo(3,2,4), and Ro(4, - 1,- 2).…

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Q: 3. Find the area (in sq. units) bounded by the parabolas x²-2y = 0 and x2+2y-8=0.

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Q: sec =zydy

A: Given

Q: -6(х— sin "x)(csCx «)(cs 3 CSC X |

A: Topic:- function and trigonometry

Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.