Exercises Distinct Real Roots of Auxiliary Equ d the general solution 1. (D² – 9)y = 0 5. (D² – 1)y = 0 %3D %3D

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -…

A: The given ellipse has Foci 0,±2 and vertices 0,±6

Q: ||r(t) x r"(t)|| ||(t)||' Use the formula K(t) to find k(t). r(t) = 4 cos(7t)i + 4 sin(7t)j+3tk %3D…

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Q: dP/dt= P(P − 10),

A: answer is in next step

Q: L (7+ 4)(x + 3)dæ = 74/3 %3D Select one: O True O False

A: The given integral,       ∫-11x+4x+3dx=743

Q: Determine if the following functions are odd, even, or neither. Provide reason. (a) f(x) = x² (b)…

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Q: 2. Evaluate f'(5) for y = v2x² – 1 hor Ju OIT

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Q: 3 dy Зу =-sin -1 2 - sin +C V4-9y2 3 A) True B) False

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Q: Find the standard form of the equation of the parabola with the given characteristics and vertex at…

A: The directrix is the line y =-3, this is a horizontal line. The vertex is at the origin (0,0), so…

Q: dx xV4-x?

A: Explained below

Q: 3. Evaluate the integral 7/4 1 + cos²0 do cos²0

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Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: Find the area of the enclosed region bounded by the graphs of y=e^x, y=x, the y-axis and the line…

A: Here we have to find the area of the enclosed region bounded by the graphs of y=ex,y=x,the y-axis…

Q: Of the Sollds gene by Volving the regions Doundeu by graphs of equation given iines. y = 3x2 y = 0 X…

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Q: For bER, b>0, b÷1, which of the following is not a property of the exponential function f(x) =b*? A.…

A: We  have to find out about exponential function

Q: lve each of the given LDE of order n. D² +6D+9)y=e³* (Use Reduction of Order Method)

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Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx x²V4-x2

A: The given integral is 1/[x2 sqrt(4-x2)].

Q: dy Find for dx 5) y = sec-(2e3x)

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Q: The most conveneient way to evaluate x² – 4 by substitution is to let x2 – 4 =y A True B False

A: On solving this we will get

Q: A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: The equation y? = cx is a general equation of A. y' = 2 B. y = 2x 2x C. y' = y y D. y': 2y O A NONE…

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Q: At the beginning, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: let weight is exponential growth function

Q: At the beginning, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: we have to find weight at t=10 hr.

Q: S- x+dx Using trigonometric substitution, (1+x?) tan4ode A sece В None tan+Od0 sec20 sin4ode (D coso…

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Q: 3. Find the area of one of the sine curve.

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Q: S- 3 dy 3y - sin n -1 4-9y2 3 A True B False

A: We have to find out

Q: T/3 sin4xdx = 4 T/12 Select one: O True O False

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Q: Find the area bounded by the indicated curves. x = 2y2 - 1, x = y2 + 8 For visualization, input the…

A: Topic:- application of integration

Q: Find the area of the region bounded by y = (1/8)(-x2 + 6x + 7) and y = -6.

A: Solved below

Q: Find the quotient of the complex numbers. Leave your answer in polar form. co cos

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Q: Find V x (V x F) if F(x, y, z) = xyj+2xyz k. V x (V × F)

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Q: | tan° xsec* xdx 6 2. Use 1 + tan² x = sec? x to evaluate

A: Solution:

Q: Evaluate the line integral g. y² dx – x²dy, where Cis the positively oriented circle of radius 2…

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Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

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Q: x++ dx 1.

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Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

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Q: Find the area bounded by the indicated curves. y = (x - 1)2, y = 8x - 24, where 3 s x s 5 Optional…

A: Let us draw the graph.

Q: Evaluate the line integral |-ydx + xdy along the curve C: y = 30x from (30, 30) to (0,0). %3D NOTE:…

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Q: S. dx 2. x²V4-x2

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Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula K(t) to find K(t). r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: So 32 (2 + 4)° da = 5120 Select one: O True O False sin4xdx = 4 7/12 %3D Select one: O True O False…

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Q: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: (D5 -D* – 2D³ +18D² –31D+15)y =0

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Q: 1. How fast is the ice forming when t = 1? When t = 2? Give units. when t = 1: when t = 2: 2. If ice…

A: see below the answer and explanation

Q: 1. Sx³Va? – x²dx

A: We have to integrate

Q: Find the partial derivative. f(p, q) = e=

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Q: y" + 9y = 9 sec² 3t, 0<t < T/6

A: To solve the following differential equation

Q: dx tan x +sin x+1

A: Solution of the problem as follows

Q: Indicate whether the following statements are True or False (write T for True or F for False in the…

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Q: Express the derivative in "subscript" notation. NOTE: Your answer should take the form fo.

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