(a)Find the equation of the tangent line to the curve 8x'y - 5x? + 7y° = 10(x-3y), at the point (2,-2). e*; -3x. (b) Given that f(x,y) = 6x³y³ - cosx + 5y-siny + 10x²- find f; fw i fy; f %3D ух

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A: The equation of the  tangent line for the function f(x) at the point x=a is, y-fa=f'ax-a. The…

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A:

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A:

Q: (b) Find the equation of the tangent line to the curve 8x²y3 – 5x2 + 7y3 = 10(x – 3y), at the point…

A:

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A: Solution:

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A:

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A: The acceleration of a particle is…

Q: 1) Find dy/dx by implicit differentiation.   sin(x) + cos(y) = 7x − 4y

A:

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

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A:

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A: Given: The function represents body mass index(BMI) is  Bw,h=wh2 where, w means weight in kilograms…

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A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

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A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

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A:

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A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

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A: We have to find

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A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

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A:

Q: The equation of the tangent to the curve y=4+ sin' x at X=0 is O y = 4 O y = 2 O y = 6 O y = 3

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

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A:

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A: Answer

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A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

A: Now point on the function is (0,6 ) . Step 1 : find the value of the derivative at x=0 . So, f(x) =…

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A: To find the equation of tangent line of the given graph.

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A:

Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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A:

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A: This question is related to differentiation, we will solve it using given information.

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A:

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Q: Find the derivative dy/dx of the Archimedean spiral.

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.