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Q: 1 2 3x2

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Q: representing all lines passing thru (-1,1)

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Q: (v®) do 1 sec J2

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (8,...

A: The objective is to find the equation of the plane. 

Q: I. Find the first derivative of the given function. 3 5. v = (1+ sin*y)

A: We can solve this as follows:

Q: - x cot 2y × CsC 2り Csc zy %3D dy

A: Integrating factor of the ODE of the form, dydx+y*f(x)=g(x) is given by, I.F= e∫f(x)dx ∫cot(mx)dx ...

Q: Problem #7: Use the chain rule to find the value of dz when t 5. = 2 4x2- 5y, x = 2+5, y = 3t– 4

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Q: a(sin 2a+cos a sin 2a) lim 1-cos² a a→0

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Q: If, when the temperature of the air is 290 Kelvin, a certain substance cools from 370 Kelvin to 330 ...

A: Given problem:- If, when the temperature of the air is 290 Kelvin, a certain substance cools from 37...

Q: (* + 2)(r – 8) f(x)=- 6)(s + 4) x =-6, x= 4 h(x)3=

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Find the antiderivative of the function f(x) = x'. That is, find a function F(x) for which F' (x) = ...

A: Given problem:- Find the antiderivative of the function f(x) = x7 That is, find a function F(x) for ...

Q: True or False. If the statement is true, write TRUE and provide a proof. Otherwise, write FALSE and ...

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Q: en the graph of the function and the x-axis over the given interval, using the prem of Calculus – 2 ...

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Q: 11 а а? A = |1 b b² c2 %3 (b — а)(с — а)(с - b) |1

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Q: The following curves bounds a certain area: = 4x – x2 - = 4 and x = -2 %3D etermine that area.

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Q: dy dr * = 1+ ev-z+5 e + e®+y

A: Option -3:C=x e-5-ex-ydifferentiating w.r.t. x;0=x (0) + e-5(1) +exe-ydydx                -ex-y0 =e-...

Q: V9-4x2 The integral of the given function dx is x2 -19-4x2 а. 2x ArcsinA + C -V9-4x b. 2x - 2Arcsin ...

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Q: (1+ ye" + xye")dæ + (xe² + 2)dy = 0 C = xye² + 2y+ x C = xye" – 2y – x %3D - Option 3 O Option 4 C =...

A: ANSWER: Option 3.  

Q: (x²+6y²)dx – 4xydy=0

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Q: (k) / te'dt (1) / e' sin(t) dt (i) e2t dt dt 1+ t2

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Q: 2x²+3 (교2+1)2

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Q: Find the particular antiderivative that satisfies the following: H'(x) = 6/x^3 - 10/x^6 ; H(1) = 0 ...

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Q: V7 dx . 3+x4

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Q: The integral of the given function fł-16) dx is v-16 +C a. Vx - 16 - 6Arcsec+ b. Vx - 16 - 6Arcsin+ ...

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Q: 5. x = 8- y², x = y2 – 8

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Q: If f(x, y) = 7xe5y + + 7y lnx, then is given by: 35e5y + 5/x 49e5y + 7/x 25e5y + 7/x 5లోbw + 7/a

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Q: y = 2xy – x y = e*C + } In(2y – 1) = –x²+C Option 3 Option 2 In(2y + 1) = -a² + C O Option 4 O None ...

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Q: A body at a temperature 0 degrees Fahrenheit is placed in a room temperature is kept at 100 degrees ...

A: Given query is to find the time required to reach the temp to 50° Fahrenheit.

Q: 0. -10 0 -101 -5 0 B = -2 10 2 6. 4 -5 -4 -2

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Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 1,...

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

Q: What is the instantaneous rate of change of f(x) = 3x + 5 at xo 1?

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Q: Find the average value of f(x) = over the interval [1, 3]. %3D (2x² + 3)²

A: The objective of the question is evaluate the average value of the given function.

Q: Find the indefinite integral. (Use C for the constant of integration.) cos. de e2

A: We will find the indefinite integral as following.

Q: given the vector field A(ρ,φ,z)= cos(φ)*ρ+ e^-6z *φ+ 6*z find the laplacian and evaluate it at the p...

A: We have to find the Laplacian at the guven point.

Q: 2n tan h 3x 3-) Arc sin tanh X

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Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The...

A: To find the length and width of the rectangle that has perimeter of 32 with maximum possible area. L...

Q: 7. y = 4 e2x, 4th derivative 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative

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Q: xydy - (y – 3x²) dx = 0

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Q: d Use quotient rule to prove [cscx] = -cscxcotx. dx

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Q: Assignment: Determine the derivative of the ff. functions. 1. y = 8x5 - 2021, 5th derivative 2. y = ...

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Q: Applications of Differential Equations A certain radioactive material is known to decay at a rate pr...

A: Let's find. 

Q: Find the exact length of the curve. 1 y = 1 <x < 3 4x

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y, (6, 0, ...

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Q: Find the area of the surface generated by revolving the curve x in the interval 2 Osys In6 about the...

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...

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Q: Find the solution of the initial value problem y" + 2y' + 5y = 24e cos(2t), y(0) = 8, y'(0) = 0. y(t...

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Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: Find the average rate of change of f(x) = x² – 1 on the interval[-1,0.4]. Give your answer in decima...

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Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a right triangle with ...

A: A rectangle is inscribed in a right triangle. The base of the triangle is a=12 inches and height of ...

Q: Consider the following function and express the relationship between a small change in x and the cor...

A: Given; fx=e3x And dy=f'xdx   ...1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'...