Given the initial condition y(0) = 2, what i the particular solution of the equation √x - √ (x² + 1.587) ³ y = = 0? ||

Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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Q: 9. TC/2 (3 sin² t cos ti+ 3 sint cos² tj + 2 sint cost k)dt

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Q: Use L'Hopital's to determine the limit. lim Oo O1 ○ -1 enx ~|-1 as x approaches co

A: This question can be solved using the concept of L' Hopital's Rule and derivatives.

Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform thickness. If the…

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Q: Q2: Solve the following f (1) 7x² +14+15 (x²+3)(x+7) dx :

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dy Q5: Find for the following functions: dx (3) y = et sin²x In√x

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Q: (C): It w = tan x and x = 4t³¹ +t: Find d?

A: Given that w=tanx  and x=4t3+t. We have to find dwdt. We can write,  dwdt= dwdxdxdt  [ using chain…

Q: Given F(x) below, find F'(x). Provide your answer below: F(x) = I 4 (414 + sin* (t)) dt

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Q: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and…

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Q: 3. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: This question is based on finding solution of inequality.

Q: Find the general solution of the following differential equation. y" - 4y + 7y=0 NOTE: Use c₁ and c₂…

A: Given y''-4y'+7y=0

Q: Sketch the function. v(x) = 0.2(x-3)²(x+2)³

A: We can answer the question as below.

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: parametric

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Q: Q2/A Cylindrical tank with radius of (3 m) and height of (10 m) has initially filled with water. In…

A: Please see the below picture for detailed solution.

Q: Find the average rate of change for the function over the given interval. y = ex between x = -2 and…

A: topic- average rate of change of function over interval Note: As per bartleby guidelines,we are…

Q: Evaluate INIM -6 x³ dx √x²-9

A: To find out the definite integral.

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

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Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: Let g(x) = = f(1) dt, where f is the function whose graph is shown below. At what value of x does…

A: Given: gx = ∫0xftdt Using Leibniz integral rule, we get g'x = ddxxfx -  ddx0f0 g'x = fx

Q: f" s [0, π]. Also, find the smallest value of x at which the average value occurs. Given that sin…

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: To find derivative.

Q: Question 1 Given the series: 2³-(²3)* Σ5. k=0 k does this series converge or diverge? diverges…

A: The objective of the question is check the converges of series and determine the  sum of series .

Q: 0²1' (19²¹) = (1) 1

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Q: What is the general solution to ya dy dx ○ y = ±₁/2. + C 4x In(4) o y = +. o y = o y = + 4x In(4) +…

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Q: 1. Solve the differential equation dy dx + 2 Y sin r 22

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Q: e −1 -1 lim (−1) t⇒0 t

A: Use limit expansion

Q: given the surface revolution x^2+z^2-5y=0 find the equation of its generating curve in the yz-plane…

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Q: Discuss the topic from algebra you used in completing this exercise. Give an example of a business…

A: Concept: Algebra: The area of mathematics known as algebra aids in the representation of…

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: Given that f(x) = h(x) x5 f'(-1). Show your work. -, h(-1) = 4, and h' (-1) = 7 find

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Q: dw (C): If w = tan x and x = 4t³ + t ; Find dt

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e…

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Q: Simplify the following witfacet casing the conjugates of the debominator 1-) 25 3+4i

A: Since you are asking multiple questions. We are answering only the very first question as per our…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

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Q: 2. Integrate the rational function below without using partial fraction decomposition. S -dv

A: Integrate the rational function below without using partial fraction decomposition v2/(v6-1)

Q: Q5: Find dy dx (1) In(x - y) = xy + y³; for the following functions: (2) y = tan³√/cot(7x);

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. cos(A) 0.49 X…

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Q: 1. / (1 + 3x) dx 5 2. / u² (4 + u°) ³ du

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Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and…

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Q: surveyor standing 57 meters from the base of a building measures the angle to the top of the…

A: distance between surveyor  and building is 57 meter angle with building top = 38 angle with top of…

Q: 3. The radius of a sphere ball is measured at r = 25 cm. Estimate error in the volume and surface…

A: The radius of a sphere is measured at r = 25 cm. We have to estimate error in the volume and surface…

Q: Evaluate the indefinite integral as a power series , x² ln(1 + x)

A: We want to find the indefinite integral as a power series.

Q: Determine the intervals on which f'(x) is positive and negative, assuming that given figure is the…

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Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

Q: Find the order 3 Taylor polynomial T3(x) of the given function given. Use exact values. 6 f(x) = (5x…

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Q: Q5: Find dx for the following functions: (1) xcinh 2x coch 2x (3) y = e* sin² x In√x

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Q: Q4: Answer two only: 2 1 -1 (A): I A=2 -2 Find AB and AC : - 1²/2 3 11 -2 -2 and 2 -- }

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Q: (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g)…

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