How would you find the derivative of sin (z^6) + sin^6 (z) using the chain rule?

Q: 2. Form the differential equation by eliminating constants a and b from y? = a(b – x)(b+ x) + 59.

A: y2=a(b-x)(b+x)+59

Q: id the Domain ol y= Tx-31 (x¢4/

A: Follow the procedure given below. Domain means value of x that defines the function.

Q: sin² 3y 5. ye 3^cot3t

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Q: f (x) = 2x? + 10, g(x) = 4x + 16

A: Topic:- geometry

Q: A team of medical researchers determined that t days after the epidemic started N(?) = 10t^3 + 5t +√...

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Q: Agree. Disagree 1. Is it correct to say that we can only get an estimate of a limit? Why do You say ...

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Q: 1.Determine if the following statements are mathematical or not. Provide solution.

A: Given that:                      

Q: y'dx-(xy + y* \dy = 0 1. Let the substitution v=²; y=vx; dy=vdx+ xdv

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Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x, y)...

A: Topic:- calculus

Q: c. A= (0 ) B = ( 4 (15 31 4 use the matrices above to solve A(B+ CX) = D

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Q: dy Find if dx y = 7u + 2 and u = 9x-3. dy dx Enter your ar

A: Given:    f(x) = 7u + 2       u = 9x - 3

Q: 2(x° + xy* + v)dx + (2x°y³ + 4xy° + 2x°y + x*y +2x)dy = 0: y(2) = 0 3.

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Q: The half-life of carbon-14 is 5730 years. A frozen human mummy was discovered in a glacier. It was e...

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Q: (x² – 1 Given: f(x) = {2x – 1 if 0 5 3.

A: Topic = Functions

Q: y = Vx (x – 1) u = i + ī + 4/15 y = f (r² + t + t')

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Q: az and ax az 6x3 3. Calculate the partial derivatives for the function z = - x3+3y3 み= (3x)-ズ+(18)15...

A: We know that; The Quotient rule: fg'=f'·g-f·g'g2   3). Given: z=6x3x3+3y3

Q: Find the orthogonal trajectories of the given family of line y = Ce-mx with m held fixed. %3D

A: Given: y=Ce-mx

Q: What is the differential equation of the family of ellipses with their centers origin and their majo...

A: Let us solve the problem using the basic equation of ellipse  later we will use different methods to...

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: On the graph of f(x) = cot x and the interval 2T, 47), for what value of x does the graph cross the ...

A: Follow the procedure given below.

Q: Consider the following curve. y = 3x2 13x + 1 Find the slope m of the tangent line at the point (5, ...

A: We have to find tangent line

Q: Findthe volume of the solid obtained by rotating the region bounded by the given curves. y=radicalx ...

A: Given Equation y=√x ,x=4 and y=0 

Q: 3. The function (x, y)= 8r-/4x +3y is homogenous in x and y of degree 2х 4. The function (x,y)= (x' ...

A: Here ,                We have given some of functions f(x,y) which are homogeneous in x,y so we have...

Q: 1. y’dx-(xy+ y² kdy = 0 Let the substitution y=2; y=vx; dy=vdx + xdv

A: Given that: y2dx-(xy+y2)dy=0

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A: Given problem:- Find the symmetrical equation of the line perpendicular to the plane passing through...

Q: Choose the correct graph of F(x) = 2 sin x; - < x< 2 T: Av 2 1 -1 -2

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Q: II. Application of Derivatives 3. Find the tangent line to f (r) = (2– 4x²)° at z = 1.

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Q: Center of Mass: Thin plate (region in the plane). Suppose Ris the region bounded by the graph of f(z...

A: Given:     f(x) = 4√x    Interval: [ 0 , 16 ] 

Q: Find the volume of the solid obtained by rotating the region bounded by y = x – x^2 and y=0 about th...

A: Given query is to find the volume of the solid generated. First we will find the intersection points...

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: What kind of triangle on its sides form the vertices (0, –5. 5), (1, –2, 4), (3, 4, 2). B) Calculate...

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Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous fu...

Q: d²y dy Solve: x2 dx2 + 3x+y = 4 cos (In x³) dx L: L:

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Q: Solve the following second-order differential equation: y" + 4y' + 5y = 8x sin æ

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Q: 1419857* -dx 4913*

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Q: 1. y'dx- (xy + y² }dy = 0 Let the substitution y=2; y= vx; dy =vdx+ xdv %3=

A: Since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: Chq/ Evaluate & F.dr by Stoke's theorem, Where fay+x§-cx+z)£ qnd C is the bounday of tri angle with ...

A: Stoke's Theorem : ∮F→.dr→ = ∫∫ F→.n^ dS

Q: 1. Consider the following vector, T = (-1,1), (a) Find two unit vectors parallel to v. (b) Find a ve...

A: Given,v=-i^+j^a) Find unit vector parallel to v.We know thatv^=vvv^=-i^+j^(-1)2+12v^=-i^+j^1+1v^=-i^...

Q: -20 e cos 30d0

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Q: Consider the following differential equation. y"-y'-30y 0 Verify that the functions .-5x and 6x form...

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Q: Find the volume of the solid generated by revolving the region enclosed by y = x2+1 and y= x+3 about...

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Q: Find the limit lim 14,cos(, 18z Note: Give the exact answer but not the decimal approximation (for e...

A: Given:   limx→0+x14 ecosπ18x

Q: 1 (i) lim 3n2 – 4000 のlim(- 2n2 +10000 X00

A: Topic:- calculus

Q: x^3 + 3x^2 – 1 = 0, [-3, -2] Use the Fixed-point iteration method and Bisection Method  to find solu...

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Q: . Using inclusion-exclusion find the number of ways to put 9 pairs of people in a ne of 18 so that n...

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Q: onsider the ellipse E in the xy-plane defined by the equation ax2 + y2 = 1 where a is positive. (1)...

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

A: Given: limx→0+6x+1cotx   As we know from the limit rule; If the limit is limx→afxgx and it results o...

Q: Let f be a differentiable function. If f(50) = 378 and f'(50) = 6, use a linear approximation to est...

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Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

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Q: Find the volume generated by rotating the region bounded by the curves about the specified axis. Use...

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