Find the maximum rate of change of f(x, y) = ln(x² + y?) at the point (-4, -3) and the direction in which it occurs. Maximum rate of change: 2/5 Direction (unit vector) in which it occurs: -8/25 -6/25

Q: Differentiate (x-2)2+(y-3)2=9 at (7/2, ((6+3√3)/2)). Then use it to determine the equation of the…

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Q: Find an equation of the line tangent to the graph of y = exat x = 0.

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Q: use the given condition to write an equation for the line in slope int form  passing through (4,8)…

A: To write an equation for the line in slope int form  passing through (4,8) and (7,3)

Q: To determine the weather, a meteorologist uses the function T = x^2y^3z, where T represents the…

A: Given the function T = x2y3z. Find the rate of change of temperature in the direction (-2,-1,2) and…

Q: Calculate y" and y'. y = 0²(20 + 4) y" = y" : II

A: Given function is : y = Ѳ2( 2Ѳ + 4)

Q: Find a function f so that the maximum rate of change occurs in the direction of u = (1/sqrt(5))…

A: The maximum rate of change occurs at ||grad(f)||. We are given that,       We know that the maximum…

Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

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Q: 3. Use the limit definition of the derivative to find the derivative of the functic a) f(x) = 2x² +3

A: The given function is The limit definition of derivative

Q: If a ball is thrown vertically upward with a velocity of 144 ft/s, then its height after t seconds…

A: Given s = 144 t - 16 t^2 a.Take the derivative with respect to t:ds/dt = 144 - 32 tAt the maximum…

Q: 3. y=x²-25x² + 2x

A: To find the second order and third order derivatives of given function

Q: A rocket is fired into the air from a table that is 3 feet above the ground with an initial velocity…

A: Given, Position function : h(t) = -16t2 +100t+3 a) Velocity function : v(t) = h'(t) = -32t + 100…

Q: Where does y=sinx+cosx have zero slope

A: Topic:- Calculus

Q: -(-3 y= 2³ +9r 4 3r

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Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: verify by differentiation

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Q: Evaluate y' at the point (2,2) 5x3y - 2x2 = 72

A: The given equation is 5x3y-2x2=72. Rewrite the above equation as follows:…