Find the indicated derivative and simplify. -[9x log x6] dx [9x log x] = 9x1 dx

Q: Solve the given differential equation. All solutions should be found. dy 3x² - 4y - y³ 4x + 3xy² dx…

A: Explanation of the answer is as follows.

Q: Alternative Formula for the Derivative f'(x) = lim Z-X f(z) = f(x) Z - X

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Q: Q2: Find the following limits V-V lim x418√√x+√ 友

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Q: In the year 2000, the population of a small city was 40,000. The population grows at a rate of r(t)…

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Q: السؤال الثالث Question Three * Q3. For the motion vector r(t) = et cost i + et sint j , find: (i) N…

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ = dx 7x +…

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Q: Lesson Performance Task At an amusement park, a person spends $30 on admission and food, and then…

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Q: Differentiate. G(x) = (2x² + 7) (9x+√x) G'(x) =

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Q: lim (tan x) cos x x-2 X-

A: This question is based on limits of 0infinty indeterminate form.

Q: x" -2x +x= 15; x (0) = 7, x (0) = -16

A: We have solve the given differentiable equation…

Q: ſº 5u³ – 3u³ – 9du

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Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 4x + 3 y = 16 where x is the…

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Q: 2. For the quadratic function y = -6x² + (K + 4)x+ 9, find the following: a. The Axis of Symmetry of…

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Q: Calculate the work (in joules) required to pump all water out of a full tank. Water exits here. d b…

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Q: Q4: A conical tank with Diameter of (2 m) from the top and (5 m) height. At the bottom of the tank…

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Q: b) Maximize the volume of this rectangular box. c) What are the dimensions & volume of this largest…

A: Solved below.

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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Q: Determine whether the differential equation (7x² - 2xy + 6) dx + (7y² − x² + 7) dy = 0 is exact. If…

A: The differential equation,    7x2-2xy+6dx+7y2-x2+7dy=0

Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

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Q: Find the solution of the given initial value problem in explicit form. 1 y′ = (1 — 13x)y², y(0) = 6…

A: We can solve the given initial differential equation .

Q: Sketch the graph of the floor function f(x) = [x+3] over the interval [-4, 2].

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Q: state the order of the given ordinary differential equation. Determine whether the equation is…

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Q: 13. The graph of y = f(x) and y = g(x) are shown below. g(x) 6 (a) (b) f(x) 2 10 -2 Find h'(9) if…

A: Explained below

Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: B)Solve the differential equation = x - y. dx

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Q: 04:B/ Simplify Moivre's theorem? [cos 30+ i sin30 15[cos 0-i sine 1³ [cos 50+ i sin50][cos 20-i…

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Q5) Find dw/dt at the given value foe the following functions 2) w = 2ve* - lnz.x = ln(t+1), v =…

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Q: 17. A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the…

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Q: Find the derivative of f(y) = 2 sin y + sin² y and then use it to find all coordinates on the graph…

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Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 5x)y², y(0) = 8…

A: Topic = Differential equation

Q: For the following flux rules, determine regions of the real line where u is instantaneously…

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Q: A particle is moving with velocity v(t) = t2-9t + 18 with dista seconds inclusive. The position at…

A: To find the time interval when partical moving right .

Q: a) Find the growth rate. The growth rate is b) Find the population after 9 yr. The population is…

A: The population p of a small city is given. We have to find the growth rate of population.

Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

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Q: b. ·(b³ + a³) units³ 3 d. -b³ + a³) units³ 16. The arc length is defined as if y=f(x) is a smooth…

A: We have to find the arc length of the curve y=f(x).   According to guide line we solve only one…

Q: need helping understanding this concept And why each statement is false or QUESTION 1 Check all…

A: We have to consider the given statements are true or false according to the given information

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

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Q: Q4:B/Simplify Moivre's theorem? [cos 30+ i sin30 15 [cos 0-i sine 1³ [cos 50+ i sin50 ] [cos 20-i…

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Q: 0 3² 3x - 4x dx 5x

A: Basic identities of integration are used.

Q: (a) (b) 2x3/2 7x² 2 7x + 9 lim x-00 lim x→ 2x3/2 3/2 +9 2x3/2 lim x+00 7√x + 9 7x 11

A: We know that when x tends to ∞, 1x tends to 0.

Q: Find the x-intercepts (horizontal intercepts) of the function: f(x) = 2|x − 1| – 8 The intercepts…

A: To find the x intercept of a function y= f(x) ,set  f(x) =0 and solve for x .

Q: State the order of the given ordinary differential equation. (1-x)y" - 5xy' + 2y = cos x Determine…

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Q: Find the equation of the line L2, pass through the point (2,-1) that is parallel to the line L1…

A: The line L2 pass through the point 2,-1 that is parallel to the line L1: 2x+4y=12

Q: 63 x dx 3√ √x²+1 S √(x² + 1)² + C Option 1 O (x² + 1)² + C Option 3 213 √(x² + 1)² + C Option 2…

A: We have to evaluate ∫x dxx2+13.

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ − 2x² + 4)

A: In this question, we want to differentiate the given function f(x).

Q: (b) y = e, y = ²x, x=0, x= ln 2 1 (c) x = =, x = 0, y = 1, y = e Y (d) y = 5x - x², y = x (e) y =…

A: Using vertical strip

Q: 2x² + 3 Find f'(x) given that f(x)= x² - 5x+2 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ -…

A: I am attaching image so that you understand each and every step.

Q: Fill in the blank. The symbol C₁ represents a constant. - (6 + C₁e-⁹x)= Write this result as a…

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