dx x√√x4 - 4 S

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: 2ydx + x(x² In y-1)dy=0

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Q: 13. What is 2sinx cos x dx? TRONG A. +C In 2 C. 2 cos.x B. +C 2sinx In 2 D. In 2 14. Which of the…

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Q: d³y d²y dy+y=0 dx3 dx² dx

A: d3ydx3-d2ydx2-dydx+y=0                (1)LetD=ddxTherefore   equation (1)…

Q: 1. x²y' + 2xy-5y³ = 0

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Q: 6.S dx √1+√√x

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Q: rocket is launched from the ground at an angle of 0.65 radians, and the rocket travels in a straight…

A: Given query is to find the height of the rocket.

Q: Find the area region bounded by the loop of y^2 = x(5-x)^2

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Q: Let f(x)=x²-x²-1 and Xo = 1. To the nearest three decimal places, find X5 using Newton's method of…

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Q: Activity: 1. Compute the area of the surface formed when f(x) = 2√1-z between -1 and 0 is rotated…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the critical number of the function defined by f(x) = x² + 4x O-1 and 0 are the critical…

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Q: Find the volume of the solid generated when the area bounded by the curve y^2 = x, the x-axis and…

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Q: Find the total mass of the wire with density p whose shape is modeled by r. r(t) = t²i + 2tj + tk,…

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Q: Let f(x)=√x - 3 on [4, 12]. Find all numbers c in [4, 12] for which the derivative is equal to the…

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Q: Find the arc length L of the graph of r(t). r(t) = t3 i+t p j+126t2 k, 3≤t≤6

A: r(t)=t3 i +t j+126t2 kdxdt=3t2dydt=1dzdt=252 t3≤t≤6

Q: Calculate the derivative. g" (0), g(s) = es S+7 (Give an exact answer. Use symbolic notation and…

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Q: X √2x²-4x-7 dx

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Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

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Q: A cylindrical can, open at the top, is to hold 300 cm³ of liquid. Find the height, h, and the…

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Q: Find the area between y = 8 sin x and y = 10 cos x over the interval [0, π]. Sketch the curves if…

A: We have to find out the area bounded by the two given curves.

Q: A toy racecar moves along a circular race track with a radius 2.6 feet long. The car starts at the…

A: Let's find.

Q: Solve the following differential equations 1. (D^2 - 3D +2) y = 2e^-x + 8 2. (D^2 - 4) y = 8e^2x -…

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Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

Q: 1. fx² In x dx = f x² dx f ln x dx =(lnx-1) + C 3 Is the solution correct? If your answer is yes,…

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Q: 1. x +4 √x -dx

A: We will use substitution method.

Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

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Q: Verify Green's Theorem by evaluating both integrals ƏN [ 1² dx + 2² dy - [ ] (™N - OM) a dA ax ду…

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Q: A model for the spread of a rumor is given by the equation p(t)= 1/1+ae^(-kt), where p(t) is the…

A: Given problem:- A model for the spread of a rumor is given by the equation p(t)= 1/(1+ae-kt)…

Q: Find a simple closed curve Cwith counterclockwise orientation that maximizes the value of { v²dx + (…

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Q: 2. 2 ydx + x(x² In y-1)dy=0

A: Solution is given below:

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

A: Given :

Q: dy 1. = e3x+2y dx X = 8; y = 1

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Q: f(x² - 8x +21)²

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Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

A: Here, we just need the complete square for the factor in the denominator (40-6z-z2)

Q: Let f(x) = 3x5 - 5x³.

A: The given function,   f(x)=3x5-5x3

Q: Solve the following X 1.0[₁-2x] i. D ii. D[xln (2x) ] iii. D[cosx – 3 sin (2 x) ]

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Q: Σ (1 + 28) n=1 n =

A: Solution: ∑n=1∞(1+x8)-n is an infinite geometric series with the first term b=1x8+1 and the common…

Q: Estimate the integral 2de using a left-hand sum and a right-hand sum with n = 3 subdivisions.…

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Q: [2 2x³ (x² − 1)² – dx|

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Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7…

A: Let's find.

Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

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Q: Solve the following X 1.0[₁-2x] i. D ii. D[xln (2x)] iii. D[cosx - 3 sin (2 x) ]

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Q: Quiz 2.2- Integration by Substitution Evaluate the following and post your answers in the g.…

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Q: Let the function f be continuous and differentiable for all x. Suppose you are given that f(-1) =…

A: Given that f(-1)=-3  , f'(x)≤4 we want to find the largest possible value of f(5)

Q: -The Bernoulli's form of the differential equation 2x'dy-y(y² +3x)dx=0 is

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Q: compute the area of the surface formed when f(x) = 2 + cosh (x) between 0 and 1 is rotated around…

A: Given problem:- compute the area of the surface formed when f(x) = 2 + cosh(x) between 0 and 1 is…

Q: Solve the following Bernoulli's differential equations. 1. x²y' + 2xy-5y³ = 0

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Q: KE-5 f(x) g(x) Find the area enclosed between f(x) = 0.6x² + 10 and g(x) = x from x = −5 to x = 3.

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Q: Rewrite the following series using the E-notation. 1 1 1 1 1 + + + + + + 10 17 26 37 12

A: Solving

Q: Using trigonometric substitution to evaluate:, find t * St³ (3t² - 4)ždt, O t = (2/V3) tang O t =…

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