Start your trial now! First week only $4.99!*arrow_forward*

Question

Assume that all the given functions have continuous second-order partial derivatives.

If *z* = *f*(*x*, *y*), where x = r^{2} + s^{2}and y = 5rs, find ∂^{2}z/(∂r ∂s).

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: Calculus Question

A: Click to see the answer

Q: section 14.6 question 12

A: Click to see the answer

Q: From the book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications by DENNIS G. ZILL...

A: Given: y'' +x2y=0 ......... (i)

Q: please help! the answer I got (-78,30,-78) is wrong

A: Equations are x+2y=-18 ...(1)x-z=0 ...(2)x+3y-2z=-12 ......

Q: Please help, thank you so much!

A: Population grows at the rate proportional to the population. In year 2000, population is 6115 millio...

Q: Can you help me solve this problem?

A: Click to see the answer

Q: 5x+4 lim X=-0 V9x2 –1 X =00

A: Consider the limit: limx→-∞5x+49x2-1 Expand the fraction: limx→-∞5x+49x2-1=limx→-∞5x9x2-1+49x2-1=lim...

Q: -2- -4- -5+ The graph above shows the velocity of an object as a function of time. Time is measured ...

A: Displacement = velcity x time (a) initial location at t=0 is 0 meters location after 3 seconds: look...

Q: Text Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications by DENNIS G. ZILL C...

A: Answer is 4+t^4/4-e^(-8t).

Q: The question is attached

A: Click to see the answer

Q: For the following exercises, find dy/dx for each function. 228. y=(3x^2+3x−1)^4

A: The given function y=3x2+3x-14 Differentiate both sideds with respect to x using chain rule dydx=d3x...

Q: P(x) = -4x2 + 1520x - 38000 (a) What is the actual profit realized from renting the 61st unit, assu...

A: Here the function represents the total profit. So in order to find profit realized from 61st rent, w...

Q: Locate the stationary points of the following functions and categorise them using second order infor...

A: Given, The stationary points are at point where,

Q: For each of the following exercises, decompose each function in the form y=f(u) and u=g(x), and fin...

A: Click to see the answer

Q: Assume that f is a one-to-one function. (a) If f(1) = 7, find f-1(7). %3D (b) If f-1(4) = -5, find f...

A: The inverse of the function exists if and only if function is one-to-one function. Assume the functi...

Q: From the book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications by DENNIS G. ZILL...

A: Click to see the answer

Q: From the book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications by DENNIS G. ZILL...

A: Given, the system of equation We have to find the solution of this system.

Q: Use calculus to determine the x-values in the domain of the following function where the tangent is ...

A: Click to see the answer

Q: & 2) Detesmine the vector, parametric + and cartesianeguatienef the lne passing throagh the co-ordin...

A: Click to see the answer

Q: Tutorial Exercise Evaluate the indefinite integral. Ter V16 + eř dx Step 1 We must decide what to ch...

A: Click to see the answer

Q: A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base wi...

A: Let x be the distance batter runs and D is the distance between the second base and the batter Lets...

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answers...

A: Click to see the answer

Q: By natural increase, a city whose population is 40000 doubles in 50 years. There is a net addition o...

A: Let x be the number of population present at any time t. dxdt=kxdxx=kdt Integrate both the sides. ln...

Q: A curve is given with x cos(pi x y) = x + y + 1. Find the tangent line and the perpendicular line to...

A: Click to see the answer

Q: For the following exercises, use the graph of y=f(x) to sketch the graph of y=f−1(x), and use part ...

A: Click to see the answer

Q: Find the equation of the tangents to the curve y = sin x at x = - T, 0, and ,. Graph the curve over ...

A: given curve y=sinx to find equation of tangents at x=-π,0,3π2 also, to draw the graph of given curve...

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and p...

A: Click to see the answer

Q: 3. Compute the following limits. Justify your steps. 2t sin(x – 1) (а) lim t→0 tant (b) lim I→1 x2 –...

A: Answer of (a). 2 (b). 1/2

Q: section 14.6 question 10

A: Given equation is z4+z2x2-y-3=0. Partial differentiation of given equation with respect to x, ∂∂xz4...

Q: solve the math by showing steps properly .

A: Click to see the answer

Q: The question is attached

A: Click to see the answer

Q: barge, as shown. If the length of one cable is D- 202 ft y the two cables. (Kound your answer to the...

A: Click to see the answer

Q: Find the global maxima and minima of the following function f(x,y) within the closed region bounded ...

A: Given data: The expression for the given function is f(x,y)=6x2+y2+2xy. The given radius of the ci...

Q: 1) Determine whether the equation defines y as a function of x. y2=3-x2 2) Find the domain of the ...

A: NOTE We’ll answer the first question since the exact one wasn’t specified. Please submit a new quest...

Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). 2 f(x) = 2x + 3x - 2 ...

A: Click to see the answer

Q: Find the volume generated by revolvingthe area enclosed by the curve x2 + y2 = 16 aboutthe y-axis.

A: Given Data: Curve: x2+y2=16 The figure below indicates the graph of the curve. The intersection...

Q: A thermometer reading 18 ∘ F is brought into a room where the temperature is 70 ∘ F; 1 minute later ...

A: Given that, A thermometer reading 18°F is brought into a room where the temperature is 70°F. The th...

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters. On...

A: Click to see the answer

Q: Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Ea...

A: Finite Math has 90 students Applied Math has 80 students The department will offer 170 sections in a...

Q: Locate the stationary points of the following functions and categorise them using second order infor...

A: Given , Condition for stationary point is, Differentiate the above expression with respect to x. ...

Q: A bucket begins holding 10 kgs of sand. The bucket is to be lifted to the top of a 20 meter tall bui...

A: Given that: Bucket begins hold = 10kg Length of rope = 20 meter Density of rope = 0.1kg/meter The we...

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

A: Click to see the answer

Q: A box has a length increasing at a rate of 2 in/s, a height decreasing at a rate of 3 in/s, and a wi...

A: Click to see the answer

Q: For the given function, find f(x+h)-f(x) / h f(x)=3 x square + 6

A: Given functions is fx=3x2+6. Obtain fx+h. fx+h=3x+h2+6=3x2+2xh+h2+6=3x2+6xh+3h2+6

Q: Please help, thank you so much!

A: Given: y=x3-12x2+36x

Q: x - 8x - 9 Find the limits in a) through c) below for the function f(x) = Use - o and ∞ when appropr...

A: Click to see the answer

Q: an) Determine the vecter equation.of the line af intersection of the twu planes = -l 3x+ Zy +4Z X ty...

A: given that two planes 3x+2y+4z=-1 and x+y+z=1. we need to find the vector equation for the line of i...

Q: 1 Find the derivative of f(x) = 2x + 3

A: Click to see the answer

Q: 1. Use the limit definition to find f'(x) for f (x) =

A: The limit definition of derivative is given by, f'x=limh→0fx+h-fxh here fx=1xfx+h=1x+h

Q: At t=0, a sealed test tube containing a chemical is immersed in a liquid bath. The initial temperatu...

A: Consider the given information, Tm=100-40e-3t