III. Derive the following HCA 1. The unity rule: = 18 dx du dx 2. The quotient rule: xp dx

Q: Find the distance between the point and the line given by the set of parametric equations. (Round yo...

A:

Q: Solve the seperable differential equation 2yy' = x. Use the following initial condition: y(2) = 2. E...

A: We can solve the differential equation as below

Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (3, 0) Vg(3, 0) =

A:

Q: By applying Rolle's theorem, check whether it is possible that the function f(x) = a° + x – 6 has tw...

A:

Q: Find the directional derivative of the function at P in the direction of v. V2 f(x, y) = x³ – y³, P(...

A:

Q: Find the specific nth term in the expansion of the binomial. (x+y)^15, n = 4

A: topic- binomial series

Q: A spherical snowball is being made so that its volume is increasing at the rate of 8ft^3 min/ Find t...

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

A: We need to find parametric and symmetric equation.

Q: 2. Find a particular solution to each of these ODES by using the method of variation of parameters: ...

A: Let's find. 

Q: Let y 522 + 2x + 3. If Aæ = 0.4 at x = 3, use linear approximation to estimate Ay Ay =

A:

Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

A:

Q: e)S 2х-4 dx х3+5х

A:

Q: 4. Determination of Integrating Factors: Solve the equation y (4x + y) dx – 2 (x² - y) dy = 0 O 2r? ...

A: Given

Q: (T^2-x)dt-tdx =0 when t=1 x=5 Ans,: x=1/3t^2 + 14/3t please show solution

A:

Q: 3. c ² +7z+10 dz, C: |F|=1

A:

Q: Determine if the series is convergent or divergent. Show your work, and clearly state the test used ...

A:

Q: Determine whether u and v are orthogonal, parallel, or neither. u = -3i + 8j - k v = 3i + j - k O pa...

A: Two vectors u and v are orthogonal if and only if u.v =0 .

Q: 6. |x²e-2*dx

A: Solved below

Q: For the demand function Qd= a- bP and the supply function Qs=dP-c, using Cramer's rule, determine th...

A: To determine the equilibrium proce and equilibrium quantity.

Q: A data set has n items. The sum of the items is 800 and the mean is 20. (a) Find n. The standard dev...

A:

Q: ydx -(x +3y)dy = 0 Ans. x = 6y In

A:

Q: 5. Check if the following is a separable equation. dy * = xy + 1 O variable separable O not variable...

A: The detailed solution is given below Thanks 

Q: e dx

A: Definite integration

Q: Define f(x, y) = 9a? + y². (1) Sketch the level curve of this function for z=36. Draw it on an xy-pl...

A:

Q: An object is launched from ground level with an initial velocity of 50 m/s, at an angle of elevation...

A:

Q: Find the arclength of y 3x + 4 on 0 < x < 1

A:

Q: Graph the function f(x) = x + 4/x Graph the secant line that passes through the points (1,5) and (8,...

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

A:

Q: Find the point on the line y = 2x + 5 closest to the point (6, 1). The function giving the distance ...

A:

Q: the line satisfying the given conditions. If possible, also indicate the symmetric equations. line ...

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,...

A:

Q: Evaluate the following integral over the Region D. (Answer accurate to 2 decimal places). I 5( . sin...

A:

Q: Obtain the solution using Integrating Factors Found by Formulas. 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +...

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions specify...

Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote :2cosacosb=cosa+b+cosa-b12∫2cos6xcos3xdx12∫cos6x+3x+cos6x-3xdx12∫cos9x+c...

Q: Given the series 7" Σ n=1 an+1 find the ratio an (Express numbers in exact form. Use symbolic notati...

A: The value will not be 7 because the question is not asking us to find the value using the ratio test...

Q: Separation of Variables: Solve for y' = yx' O x4 = y In c Ox = cy

A: To solve the given differential equation by separation of variables  

Q: - 4x +7 on the interval [0, 4). Verify that this function satisfies the three Consider the function ...

A:

Q: Re-write. the.crthar..fie.i.texated.ntegrals. S FiXny, Z)dydzdx dzdyd X -I x2 d

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any s...

Q: cos x dx Sx x sinx cosx dx 4. 3.

A:

Q: Homogeneous Equations: Solve the differential equation xdy – ydx - x2 - y?dx = 0 arccos ((-) = In cx...

A:

Q: Use the remainder theorem to find P(-2) for P(x) Specifically, give the quotient and the remainder f...

A: To use the remainder theorem to find the quotient and remainder of the polynomial P(x)=2x3+2x2-x-3 i...

Q: Determine whether the following sequences are convergent or divergent. If a sequence is convergent, ...

A: For (a),     limn→∞ n-n2-nRationalize,=limn→∞ nn+n2-n=limn→∞ 11+1-1n=limn→∞ 1limn→∞ 1+1-1n=12 So, co...

Q: (y² – xy) dx – x²dy = 0 Ix-

A:

Q: h as suggested by the equ )dx +3(x+ 2y)dy = 0 whem

A:

Q: In Exercises 1-4, use the comparison test to confirm the statement. 1. 2 diverges, so diverges. n-3 ...

A:

Q: tan?x lim

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: To find unit vectors that satisfy the stated conditions.a Same direction as -3i+2ju=?b Oppositely di...

Q: Find the area of the triangle with vertices P(1,5, –4), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the exa...

A: We know that the expression for the area of the triangle △PQR is: A=12PQ→×PR→ The given vertices of ...

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: For solving all above parts we have to use concept of unit vector.

Q: 7.) f (x)> (3x+2)(5x-2)

A: