Q4) a) Find the tangent plane and normal line of the surface f(x, y, z) = x? + y²e* + z? = 3 at point P (0,1,1) b) Solve differential equation using Laplace transform ý + 3ý + 2y = 4 with y (0) = 0, ý(0) = 1

Q: 2. A ball is rolling around on a surface with shape given by z = f(x, y) = e-5y sin²x. The ball…

A: (a) To calculate the direction in which the ball would roll from a general point (x, y), we need to…

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Q: For an equation x" +x = 0 a) Draw a tangent vector to a solution (x(1), x' (1)) in the phase plane…

A: (a) Solve the differential equation as follows: Let p=dxdt, or, x'. Differentiate it with respect to…

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: (2) Find a smooth curve a in GL(2, R) passing through the identity such that a'(0) 1 0 Justify your…

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Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: Hiw 2 Find dy For (πCシ)

A: Differentiation of the function helps to find the derivative of the function. Simplification of the…

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…

Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the sbe and equation of the TANGENT and NORMAL LINE to the curve Graph cach curve, Kormal, and…

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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Suppose the two curves r(t) = (t,0, 1 + e' sin(t)) and q(s) = (0, s, vs² + 1) lie entirely on the…

A: According to the given information, consider the given two curves:

Q: 2 Find the Cerivative o3 a) y°(x+2)= c3

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Q: (Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x',…

A: Given that the tangent vector to and is the speed of the point along the curve at time t .Here also…

Q: a) Find dy if y² + x²y² = 1+x^y use implicit differentiation b) If x² + y² = 6. Find y' in term OF…

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Q: Find equations for the tangent plane and the normal line at point Po (Xo Yo-Zo) (5,1,0) on the…

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Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: Consider the differential equation y' = 2y X a) Sketch the slope-field for x in [−2, 2] and y in [0,…

A: Given: Differential equation y'=2yx. To do : a) Sketch the slope-field for x in [-2, 2 ] and y in…

Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00

Q: Find the general solution to the following 3-by-3 linear system: 1 -5 10 2 -4 8 X. dt 3 -5 8.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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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.