Find the general Solution For D-E (xy-4/nx+x² sin x²) dx + x² dy =o

Q: f(x) || 1 x² + 1

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Q: use € Calcus implicit different to find sy ldx Q32 y cos (ty) = 2x + 2y

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Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A: The given tablet(h)0246810r(t) (L/h)8.67.66.86.25.75.1

Q: Find the general Solution of . T NOTINTOS dy dx = 2 x e x²²

A: dy/dx = x2

Q: Use substitution to find the Taylor series at x = 0 of the function In (1+5x9). What is the general…

A:

Q: Consider f(x)=x2² and h(x) = 4x-4. A) Sketch the graph of these on the interval x= [0,3]. (Draw the…

A: Two functions f(x) and g(x) are given. We have to draw graph

Q: Find the absolute maximum and absolute minimum of f(x) = 2x³6x² - 48x + 95 on the interval [1,6].

A: f(x)=2x3−6x2−48x+95 on the interval [1,6]Using the power Ruleddxxn=nxn−1

Q: Let (a) 10.5 3.5 ・6.³.5 P f(x) dx = 9, [ r(x) dx = [ 3.5 10.5 a £10.5. f(x) dx = 4, and (b) (8f(x) -…

A: Given,

Q: The function G (t) = 30 – 8.8 cos (t) models the depth, in feet, of water t hours after 9am. Find…

A: G(t)=30−8.8cos⁡(π4t)Using the power Ruleddxxn=nxn−1ddxcos⁡(ax)=−asin⁡(ax)

Q: (Section 4.3) Your task is to estimate how far an object traveled during the time interval 0 ≤t≤ 8,…

A: The given table time (sec)012345678velocity (feet/sec)2610111417182123

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for f(x) = x² - 6x on the…

A: F(x) = x2 - 6x Interval [ -2 , 4 ]

Q: 2. A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

A: A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

Q: Find the area of the shaded region. ㅇ 쁨 38 3 이렇 이렇 (0, -3) y= (16,1) 3 16 x

A: we need to find the area of the function

Q: Let f(x) = x^4 − 4x^3 − 20  (a) Find the first derivative f'(x) and the second derivative f"(x)…

A: According to our guidelines we are supposed to answer only the first three subparts of the question.…

Q: Write and solve the differential equation that models the following verbal statement. Evaluate the…

A: We solve the given problem by using the variable-separable method.

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for fx √(x)= this interval that…

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Q: Consider that f(x) > 0 for a ≤ x ≤ b. Find the area (in units2) under the graph of f(x) between the…

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Q: Find the work done by the force field F in moving an object from P(-7, 5) to Q(5, 5). 2x. F(x, y) =…

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Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

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Q: Suppose f(0) = 4, f'(0) = 2, f''(0) = 2, and f(3) (0) = 6. Find the third-order Taylor polynomial…

A: The nth degree Taylor Polynomial of a function f(x) centered at the point x=0 is given by

Q: Solve the following integration :- 6 dx | (X-4)(+7)

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Q: Find the Maclaurin series for the given function. 3e-x

A: A Maclaurin series is given by f(x)=∑k=0∞f(k)(a)k!xk

Q: The function f(x) = x³ + 5 is

A: f(x)=x3+5

Q: Transform the given system into a single equation of second-order x₁ = −5x₁ + 7x2 x₂ = -7x1 - 5x2.…

A: We have to transform the given system into a single equation of second order.

Q: Question 3.1. Use integration by parts to solve the given indefinite integral and thus evaluate…

A: By using integration by parts to solve the given indefinite integral and thus to evaluate…

Q: 1. Evaluate each of the following derivatives. You need not simplify your answer. (a) √t (2-1)³ dt d…

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Q: Given the values of the derivative f '(x) in the table and that f(0) = 195, estimate the values…

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Q: Given that f(x)=4x-16 where f(x)=y define a function rule for f^-1. which of the following are…

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Q: -ind the curvature of r` (t) = ti + t²j + t³ k at different valu oft. Which formula would you use to…

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Q: olve the following integration:- 2 x² + 3 x(x-2)(x-6) ² dx

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Q: Express the limit as an integral. 4 lim (7(x)² - 2(x, ) ³) 4x over [0, 4] n→ ∞o Σ i = 1 dx

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Q: Evaluate the integral: /9 - x² = dx (A) Which trig substitution is correct for this integral? 0x = 9…

A: Given indefinite integral is

Q: Evaluate u³(²-1)² du in terms of u by expanding the integrand. [/u³(²-1)² du = -/( 11 + C 1) du

A: To evaluate  in terms of  by expanding the integrand.

Q: For y = xe^(-1/x), find the intervals of increase and decrease.

A: given function To find: the intervals of increase and decrease.

Q: Find the absolute maximum and absolute minimum values of the function f(x) = x + 1/ interval [0.2,…

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Q: True or False: If a ‡ b and if ſå |ƒ(x)|dx = 0, then f(x) = 0. True O False

A: The given statement is If  and if  then

Q: Graph the function y= by identifying the domain and any symmetries, finding the derivatives y and y…

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: 3+x 4. (a) Find a power series representation for the function f(x) = is the radius of convergence?…

A: The given function is

Q: F(x, y, z) = (2xz + y²) i + 2xy j + (x² + 6z²) k C: x = t²2, y = t + 2, z = 2t - 1, 0≤t≤1 (a) Find a…

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Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49

Q: A table of values of an increasing function fis shown. Use the table to find lower and upper…

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Q: Apply the trigonometric substitution x = √3 sec(0). When determining the lower limit, you will have…

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Q: The number of bacteria in a culture is increasing according to the law of exponential growth. There…

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Q: Trust Fund A deposit of $20,000 is made in a trust fund that pays 5% interest, compounded…

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Q: For t> 0 hours, let r(t) = 120 (1 - e 5 liters/hour hour, at which a car travels along a straight…

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Q: Tutorial Exercise Write the given expression as a single integral in the following form. [₁1 (2) dx…

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Q: Use upper and lower sums to approximate the area of the region using the given number of subinterval…

A: finding the area using upper sum and lower sum.

Q: Given the parabola: x = 3(y + 5)² - 4.

A: x=3(y+5)2−4We are comparing the equation withx=a(y−k)2+h

Q: Consider the function f(x) = 14x - 4sin-¹. Find the critical number(s) off in the interval [-1,1].…

A: The given function is