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g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3, x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and yt(3,4)=-100. Calculate gs(3,4)
Consider the given function and the given interval. f(x) = 5 x , [0, 4] (a)...
Estimate the area under the graph of f(x)=x2+3x from x=1 to x=4 using 33 approximating rectangles...
y'' - 8y'+ 16y = cos x
1. Consider the plane 4x+y-2z=4 and the line r(t) = < t, -2t, -tt >. a....
Where are the local max/min for the function 9sin(5πx) between x=0 and x=2/5? Do this problem...
A particle moves from point A=(0,−6) to point B=(−3,−2) in 6 hours at a constant rate....
Write an equation for the tangent line to the plane curve xy^2 − 2x^2 + 3...
Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with...
compute partial derivatives df/dx and df/dy, and all second derivatives of the function: f(x,y) = [4xy(x^2...
give specific examples... not only formulas 1. Find the derivative of the product between a scalar...
1. find the absolute maxima and minima for f (x) on the interval [a, b]. ...
The region bound by the curves y = 5 and y = x +(4/x) is rotated...
4cos^2x [0,pi] what are the absolute max and min
Find a formula for the solution of each of the following initial value problems. a) y′...
If f(x)-x^3-3x; a) find the intervals on which f is increasing or decreasing. b)find the local...
Given f(x,y) = x2−3y2−8x+9y+3xy for each and any point that is critical, use the second-partial-derivative test to...
Use the model for projectile motion, assuming there is no air resistance and g = 32...
Approximate the area under the graph of the function y = x^3: from [0,8] for n...
if y=uv, where u and v are functions of x, show that the nth derivative of...
Consider the function f(x)=3−7x2, −3≤x≤2 The absolute maximum value is and this occurs at x= The absolute...
4. For the function g(x)= 3x+3 /x2-3x-4, find any x-values where g is discontinuous. Identify each...
Find the four second partial derivatives of ?(?, ?) = ? cos ? + ??x
If the cylinder of largest possible volume is inscribed in a given sphere, determine the ratio...
how do you calculate rate of change for a side length of a cube. when the...
Consider the following: y = 3x2-6x+1 a.) Find the interval(s) of increase. Find the interval(s) of decrease....
Each time that a Martian egg hatches, there is a 43% chance that the baby is...
\int \frac{5x^2-8x+1}{\left(x-3\right)\left(x^2+2\right)}dx calculus 2
Find the surface area of the cone x2 + y2 = z2 that lies inside the...
The region R is bounded by y=x^2 and y=sqrtx. Find the volume of the solid generated...
Find an equation of the line through the point (-1,3) that cuts off the least area...
D(x) is the price, in dollars per unit, that consumers are willing to pay for x...
A stone is thrown straight up with an initial velocity of 147 meters per second from...
Find y'' by implicit differentiation. 4x^3 + 3y^3 = 5
1. Find the rate of change of y with respect to x at the indicated value...
Solve the given LDE using the method of undetermined coefficients. y'''-y'=4e^-x+3e^2x; y(0)=0, y'(0)=-1, y''(0)=2
Construct a convergent Jacobi iteration to the system x+5y+2z=2 (45+13)x-2y+10z=3 -4x+3y-(45+8)z=4, Perform two iterations.
Find an equation of the normal line to the parabola y = x2 − 8x +...
If you have the average production function: APL=3L2 - 0.05L3, find a) the first derivative for...
Find the shortest distance from the origin to the curve x^2y^4 = 1 (please do not...
Test the series for convergence or divergence. 1/ ln(2) − 1/ ln(3) + 1/ ln(4) −...
the base of certain solid is the triangle at (-4,2),(2,2), and origin. cross-sections perpendicular to the...
Find the area of the region enclosed by y = (x + 2)^2 , y =...
An airline sells all the tickets for a certain route at the same price. If it...
intetgral of e^(4x)sin(2x)dx
By suitable reinterpretation,show that 1 + 2 + 3 + 4 +···= −1/12. Please give a...
sketch the plane curve and sketch the unit tangent and the unit normal vectors. r(t)= ti+1/t...
The management of a watch company has determined that the daily marginal revenue function associated with...
At noon, ship A is 50 km west of ship B. Ship A is sailing south...
Consider the following planes. x + y + z = 1, x + 3y + 3z =...
A) Use implicit differentiation to find an equation of the tangent line to the ellipse defined...
One injection of 150mg of a medication is given to a patient. The amount of the...
Consider x = y3. Determine dy/dx in two different ways. One must be the chain rule!
The owner of the Rancho Grande has 2,988 yd of fencing with which to enclose a...
Using the definition of the derivative, find f'(x). let f(x) = x^2/x+1
A dam has a shape of a trapezoid. The height is 30 m and the width...
Let R be the region in enclosed by y=1/x, y=2, and x=3. a) Compute the volume...
Sand pours out of a right, conical container at a rate of 24 cubic feet per...
use Maclaurin series for y = cosh(x^3) to compute f(6)(0). the six diravative of f(x) evaluated...
Find the parametrization of the line through (3,9) with slope 11 for given ?(?)=2?.
A particle is moving according to the given data a(t) = sin t + 3 cos...
Consider the functions ?(?) = 5? + 3 and ?(?) = 3?^2 − 4? + 7....
Suppose the derivative of f exists, and assume that f(1) = 4, and f'(1) = 5....
Logarithms assist, among other things, in solving exponential equations in general. Understanding some logarithmic equivalences is...
solve the differential equation... (x2-1)(dy/dx)+xy=0
What is the tangent line equation for the circle r = 2cos(theta) when theta = pi/3?
Find the 4th degree, T4 taylor polynomial for f(x)=arctan (x) centered at c=1/2 and use it...
If the Maclaurin series for f(x) = e^x sin x is given by: c0 + c1...
If y=ux then dy/dx=(u+x du/dx) i need explination how we got this??
8. Consider the function ?(?) = 4 − 6?2 on the interval [−2,5]. Find the value(s)...
The hands on a clock are of length 4 inches (minute hand) and 3 inches (hour...
Find y as a function of x if y′′′+4y′=0, y(0)=3, y′(0)=−4, y′′(0)=8. y(x)= _____
Evaluate the surface integral S F · dS for the given vector field F and...
Using Euler’s formula, show that for any natural number n, cos(nθ) + isin(nθ) = (cos(θ) +...
The current population of a certain bacteria is 4952 organism. It is believed that bacteria's population...
f(x)= 12x- x^3 1. where is the local min? x-value 2. where is fhe local max?...
A particle is moving along a coordinate line with an acceleration of a(t) = 3t m/sec2....
MATHS CALCULUS I am asked to prove sinx <= x for all x>=0, by using the...
Evaluate the indefinite integral using Trigonometric Substitution. Make sure to show all your work, and explain...
Find the solution to the following system by converting the system to matrix form: x'1= 2x1+4x2,...
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