### Find the equation of the tangent at the point (x,y) on the curves: (a) (x2/a2) + (y2/b2) = 1 (b) (xm/am) + (ym/bm) = 1

Differential Calculus The Equation of a Tangent

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Differential Calculus The Equation of a Tangent

Question 1) Find the direction from (-3, 1, 2), in which g(x,y,z)=x^2*y*z-2*z^3 decreases fastest. question 2) Follow the line in the direction you found in part 1) to estimate, using linear approximation, the location of the point closest to the coordinates (-3,1,2) at which g=1;Do not use a calculator; Express the answer us

Let x = (1/2)(u^2-v^2), y=uv, and f=f(x,y) [QUESTION 1] use the chain rule to derive the change of variables formula in matrix form: (fu,fv)=A*(fx,fy) {actually it is vertical , so fu is at the top and fv is at the bottom. Same for fx and fy: fx is under fy; sorry for the notation I cant do it another way} [QUESTION 2]

Consider the function : f(x,y) = x(x-1)(x-2) + (y-1)(x-y) [QUESTION 1]find the maximum and the minim values of the directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies . ( (df/fs)]u : I can't write the symbol clearly but it means : the derivative of f according to s on the directi

Consider a triangle in the plane, with angles , a, b , c. Assume that the radius of its circle is equal to 1. 1) by decomposing the triangle into six right triangles having the incenter as a common vertex, express the area A of the triangle in term of a, b , c ( the answer should be a symmetric expression). Then use the resu

A population obeys the logistic model. It satisfies the equation dP/dt = 2/1300 P(13-P) for P>0 Assume P(0)= 3 Find P(74)

Find an explicit or implicit solutions to the differential equation: (x^2 + 4xy)dx + xdy = 0 "F(x,y) such that the solutions are F(x,y)=c for an arbitrary constant c".

The following differential equation is exact. Find a function F(x,y) whose level curves are solutions to the differential equation: ydy-xdx=0 "F(x,y) such that the solutions are F(x,y)=c for an arbitrary constant c".

The steady state deflection is given by: y''''+c^4*y=f(x) calculate and plot the deflection for a load: f = 1 for |x|<10, f=0 everywhere else. using Fourier transform. Plot the deflection for various values of c.

Limit f(x) (x to 1) and limit f(x) (x to -1), where f(x) = 1/x-1 if x < -1 x^2 + 2x if x is greater than or equal to -1

A closed box with a square base is to have a volume of 1,500 cubic inches. Express its surface area as a function of the length of its base.

Write an equation for the line with the given properties Through (2.5) and parallel to the y axis.

Find the slope and intercepts of the given line and draw a graph. X+3/-5 + y-1/2 = 1

H(u)= ^4 to the square root of u^2-4

Please see the attached file for full problem description.

Please see the attached file for full problem description. --- Let S denote the closed cylinder with bottom given by z=0, top given by z=4, and lateral surface given by the equation x^2 + y^2 = 9. Orient S with outward normals. Determine the indicated scalar and vector surface integrals.

Find dy/dt of the function y= 2/(2t^3-5)^4 Could you please explain each step required to complete this question?

Evaluate the iterated integral (See attached) SEND ANSWER AS ATTACHMENT

Here is the problem: Find the volume under the plane z = 4x + 2y + 25 and over the region bounded by y = x^2 - 10 and y = 31 - (x-1)^2

Tangent and Normal (III) (Differential Calculus) Find ds/dr for the curves: (a) r = a? (b) r = a/? See attached file for full problem description.

Tangent and Normal (II) (Differential Calculus) Find ds/d? for the curves : (a) r2 = a2cos2? (b) rn = ancosn? See attached file for full problem description.

Find the General Solution of the equations. (a) r = a2t (b) r - 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0

I am having difficulties gaining a solution for the following differential equation of x'=2t3 -6t2 + t1/2. Could I please get assistance with detailing my solution.

Use the method of Lagrange multipliers to find the indicated extremum. You may assume the extremum exists. Find the maximum and minimum values of f(x,y,z) = x + 3y - z subject to z = 2x^2 + y^2

Find the critical points of the given function and classify each as relative minimum, relative maximum, or a saddle point. f(x,y) = x^2 + 2y^2 - xy + 14y

Please see attached file for various questions in Calculus. Thank you for your help.

Laplace Transformation Question. Please see attachment.

Laplace Transformations See attached for questions

Show that equation is of exponential order and not of exponential Order. (please see attachment for details)

Solve (see in attachment) without using partial fraction decompositions. Thanks you