HiW. ation Separable Methood of Differential Eque Equatons Find the salution of the following differential equationss O ý=ky where k is Constant

Q: Flowers tend to open in the daylight and close in the dark. The percent P of flowers open during a 2...

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Q: x-1 6. f(x)= x +3x 4x 7. f(x)=-- x +4 8. f(x)=- x +6x+9 9. f(x)=-- x +1 L0. f(x) = x' + 4x + 4x + 2

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Q: Find the the arc length of y = 4x? – 2 from = 0 to x = 2 No decimal entries. Find the exact value. L

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Q: Solve the given differential equation. All solutions should be found. dy = e + 15y da NOTE: Use c fo...

A: Given:- y'=e9x +15y  To find:- General solution for given differential equation

Q: 9. cos (21) di 10. 11. sin'x cos's de 12.

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Q: If a parabola defined by f(x)=2−x2 is inscribed under equilateral triangle ABC, so that the parabola...

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Q: x+4, for x - 1 (A) Select the correct choice below and, if necessary, fill in the answer box to comp...

A: This question can be solved by using the concept of existence of limit at a given point.

Q: xarctanx dx

A: Product Rule of integration : ∫u.v dx = u∫vdx - ∫(dudx∫v dx)dx darc tanxdx = 11+x2 ∫ xn dx = xn+1n+1...

Q: sec Odo

A: ∫1tdt=lnt+C

Q: Question 16 3x3-5хе\ + 2хcos(x) dx Evaluate: None of the given choices 3x4 5ex + 2sin(x)+ C 4 © x³ –...

A: Option D) x3-5ex+2sin(x)+C

Q: Let r(x) = f(g(h(x))), where h(1) = 4, g(4) = 5, h'(1) = 5, g'(4) = 3, and f'(5) = 7. Find r'(1). r'...

A: To find out r'(1). 

Q: Evaluate the indicated trigonometric function of 0, where 0 is an acute angle determined by an inver...

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Q: The profit (in dollars) from the sale of x lawn mowers is P(x) = 20x-0.02x – 550. (A) Find the avera...

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Q: csc (tan 2y-1)cy 5. cos* 2y

A: Given ∫csc2(tan2y-1) dycos22y To evaluate the integral using Trigonometric formula:

Q: If two coins are tossed, what is the probability of obtaining at least 1 head?

A: Given two coins are tossed let H denote the head on coin  and T  denote the tail

Q: The integral of the given function | cos(9x) cos(5x)dx is equal .. 14 sin 4x + 4 sin 14x А. · + C 12...

A: This question can be solved by applying the formula of 2.cosA.cosB

Q: For the next three questions, consider the following differential equation: (2y sin x cos x – y + 2y...

A: 2ysinxcosx-y+2y2exy2dx-x-sin2x-4xyexy2dy=0  

Q: dx/y-xdy/y^2=0 solve using exact equations (diff eq)

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Q: Let f(x) = (7 – 2x)" f(x) has one critical value at A = For x A, f(x) is Select an answer

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Q: 3) Find the volume of the solid that is generated by revolving the region bounded by y= sin z cosz a...

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Q: sin(Tæ) lim x → 12 In(x – 11) -

A: The given limit,          limx→12sinπxlnx-11

Q: In x Use the change of base formula loga x = to show that In a log, x = dx x In a d d loga x = dx dx...

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Q: Evaluate the definite integral. Round your final answer to three decimals. 53 298, 512 dt 38 t3 Vt2 ...

A: We will evaluate the given integral as shown below

Q: 5. 12 y²-9dy

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Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: Consider the function f(æ) = x²e3". For this function there are three important intervals: (- 0, A],...

A: The given function is  f(x)= x2e3x  Find critical point and interval of increasing and decreasing. 

Q: Solve the system of differential equations consisting of the following equations: (D – 2)x – y = 0 (...

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Q: The total spent on research and development by the federal government in the United States du S(t) =...

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Q: If F(x) = f(g(x)), where f(5) = 7, f '(5) = 2, f '(2) = 3, g(2) = 5, and g'(2) = 3, find F '(2). F '...

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Q: Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are ...

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Q: The picture shows a combination hopper cone and bin used by farmers to store grain after harvest. Th...

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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)

A: The objective is to verify the conclusion of clairaut's theorm.

Q: -dx In 5

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Q: 1. Two particles travel along the space curves r, (t) = (t, t,t) and r2 (t) = (1+ 2t, 1+ 6t, 1+ 14t)...

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Q: 1. Complete the following statements, if s(f) is a position or displacement function. a. Average vel...

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Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex an...

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Q: Evaluate: ∫[(sin 3θ)^8][(cos 3θ)^6]dθ. From θ = 0 to θ = π/6 a. 2π/99 b. 2/99 c. π/99 d. 1/99

A: Evaluate: ∫[(sin 3θ)^8][(cos 3θ)^6]dθ. From θ = 0 to θ = π/6 a. 2π/99 b. 2/99 c. π/99 d. 1/99

Q: 2. The graph of g(x) is given below. Find lim g(x) x→9. a.0    b. 9    c.1   d.2 3. What is lim h(...

A: 2. As you can see, the graph of g(x) is continous. Therefore,                limx→9g(x)=g(9)     -(1...

Q: For the next five questions, consider the following differential equation: (y? + cy°)dx + (5y² – xy+...

A: Given differential equation is y2+xy3 dx + ( 5y2-xy+y3siny) dy =0 Also, given that M is coefficient ...

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact ...

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Q: Determine whether the series converges. 7k-1 k=1 O The series converges. O The series diverges. IM:

A: Topic:- sequence and series

Q: f the following is ion of a discreet A: Sum of two nu o boxes containir

A: We will find the discrete probability distribution. 

Q: a n п i = 6 dz EVALUATE IN TERMS OF GAMMA FUNCTION.

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Q: Find the lines that are tangent and normal to the curve at the given point. x²y? = 100, (-2,5) The l...

A: The given function is x2y2 = 100  at (-2,5)    

Q: Find the derivative of the function. h(x) = log,(x² + x) h'(x) %3D

A: Given query is to find the derivative of the expression.

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the s...

A: To find the volume.

Q: If the area bounded by the curves y = x + 1, x = 1, x = 2 and y = 0 are revolved about the axis y = ...

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Q: Find the solution of the given initial value problem in explicit form. - (1 – 5z)y", y(0) 6. y(1) = ...

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Q: What is the angle of elevation of the sun when a 41-ft mast casts a 10 ft shadow?

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Q: 9. Find all second order partial derivatives for the following functions: a) z = xe-2y + x In(y) + y...

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