Direction: Read then solve the question carefully. Click the letter of the correct answer. Boyle\T 1\textquoteright s law states that if the temperature of a gas remains constant (c), its pressure is inversely proportional to its volume. Find the rate of change of the pressure with respect to the volume. Select one: dp AP dp AP dp -c AP dp cu AP ||

Q: dx Evaluate x²V4

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Q: 4. Homogeneous Diffe rential Equation: (r+2y-4y kx-(x' -8ry-4y kdy= 0 Use the substitution x = y = w...

A:   Differential equation  are mathematical tool to define rate of change for whole equation. 

Q: 1. Elimination of Arhitrary Constant: y= Ax + Bx+C.A and B are constant, C is a parameter

A: Solution ) y = Ax2 + Bx + c  .......( 1 )  Differentiate with respect to x  y' = A × 2x + B × 1 + 0 ...

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Q: Use the equation = E x" for |x| < 1 to expand the function , in a power series with centerc 0. 3-x (...

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Q: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x . ...

Q: Based on the graph of f (x), find the following: Note: If the f(a) and lim f(x) does not exist write...

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Q: Answer 4,5,6,7 4.What is the second derivative of  y=6x^4−3x^3+x^2−5? A.y′′=144  B.y′′=72x^2−18x+2...

A: As per guidelines we can solve only one question at a time so if you need more answers kindly repost...

Q: Use Simpson's rule with n = 4 to approximate 5/ a2 + xdx Keep at least 2 decimal places accuracy in ...

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Q: Find the derivative of the function. g(t) = (e* + 1)3 g'(t) = Need Help? Read It Watch It

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Q: 2) Evaluate the integral 1 2- -2 XVX -16

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Q: Homogeneous Diffe rential Equation: (x* +2.xry – 4y° kdx– (x² – 8xy – 4y² ldy = 0 Use the substituti...

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Q: Simplify the expression: 5(1 + w) = %3D Submit

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Q: Use Double Angle Identities to simplify the following trig expressions. Your answer should use only ...

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Q: The figure on the right shows the graph off and a line tangent to the graph of f at x 8. Find f(8) a...

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Q: . Separation of Variables: x(y +1dx + dy = 0

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Q: Lqsudnhlao203=9m] -03P99E90RO[9U3RM7210 Ud8y(,om 301 29u 3 ***#!12ngwe gggd 982eh c y The function f...

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Q: 8. There is a jump discontinuity at x = 2 and f(2) = 3

A: 8. there is a jump discontinuity at x=2 and f(2)=3

Q: For what values of r does the function y = ex satisfy the differential equation y" – 4y' + 2y = 0? (...

A: We will differentiate y and put in the equation and then will find the value of r.

Q: Let y=f(x) be the solution to the differential equation dydx=x−y−1dydx=x−y−1 with the initial condit...

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Q: 11.What is the slope of the tangent line to the curve y = 3x? – 5 at poin - O A. -7 О в. -5 O C. -6 ...

A: Differential equation 

Q: dx 9. Evaluate f VI (1+x) dx Evaluate J J-x sin-1 x 10.

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Q: Homogeneous Differential Equation: (x* +2.xy – 4y² kdx – (x² – 8xy – 4y² ldy = 0 y. x==; y = wx; d =...

A: This question is based on solution of Homogeneous differential equation.

Q: (1) Let C1 and C2 be arbitrary constants. The general solution to the homogeneous differential equat...

A: Let's find. 

Q: 7. lim 4?* 8. lim e 9. lim e 10. lim e*

A: To evaluate the given limits.

Q: Which of the following is equivalent to sec B(tan?B+1) for all values of ß for which sec B(tan²B+1) ...

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Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

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Q: Given the position s(t) = 8t² – 7t + 12 of a - body moving in a line, with s in meters and t in sec....

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Q: Find the inverse of the given function. log, (æ) f '(x) =

A: Given query is to find indicated inverse function.

Q: Families of Curves: Parabolas with vertex ( h, -3) and it opens to the left

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Q: Tell if the function is continuous at given interval f(x)=; 2x +4 |-2,2]

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Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy i...

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Q: Lqsudnhlao203=9m] -03P99E90RO[9U3RM7210 Ud8y(l,om8 301 29u 3 ***#!12r Families of Curves: Parabolas ...

A: Topic:-  geometry

Q: Define S(x) to be the slope of the line through the points (0,0) and (x, f(x)) in the figure below. ...

A: We have to the value of x where s(x) minimum aur maximum

Q: Find the slope of the curve r=7-cos(theta) at theta=9pi/4.

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

Q: Find the point on the graph of the given function at which the slope of the tangent line is the give...

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Q: What is the general solution to the differential equation dx 8e4x 2 cos(2y) A 2 sin(2y) – 8e4r = C -...

A: topic - differential equations

Q: lim cos + 4

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Q: 4x 3+3x²+1 What is the general solution to the differential equation dx 3y2 y = V x4 +x 3 +x +C B y ...

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Q: . The differential equation (2x³ – xy² – 2y +3 )dx– (x²y+2x }dy = 0 is exact because ƏM ƏN %3D ôx

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Q: 5x 14 dx To evaluate the integral which of the following formulas can be used? V4+8x5 udu (bu (bu – ...

A: Let u=x5 then du=5x4 dx and a=4 and b=8 And third option is used for solving given integral. 

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

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Q: Answer 5,6,7 5.If y=(2x+7)2 , then what is  dy/dx? A.dy/dx=2(2x+7)  B.dy/dx=2 C.dy/dx=4x  D.dy/dx=...

A: Differential equation 

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Q: Q11

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Q: (D3 + 6D? + 12D + 8) y = 0 when y (0) = 1, y (0) = -2 and y" (0) = 2

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Q: 12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

A: We are asked to find a value and L values.