1 dx

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

A:

Q: 125 and y = 10. y? y = x, x =

A: answer is in next step

Q: 15. The solution of Laplace equation и + 3 0, и(х,0) — 0, и(х, п) — 0, и (о, у) — 0, и(0, у) %— 3sin…

A: Please see the below picture for detailed solution.

Q: Let y1(x) and y2(x) be solutions of the linear differential equation with constant coefficients…

A: To find  the possible solutions of given differential equation.

Q: b) S cosh(In(cosx)) dx

A: We have to find the integral.

Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

A:

Q: 2 2-y Mote: Complete lirst for X, them or Y.

A:

Q: 12 9.

A: Use Trigonometric ratios

Q: Q1: Find dy/dx of the following functions: 1. x'e? y = log2 2Vx+1 2.

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Find the relative maximum and minimum values. f(x.y)=x +xy+y° 28y + 261

A:

Q: The solution of the differential equation below is dy Зу- + 4x = 0 dx

A: This is a problem of differential equation. Based on the general formula and concept of separation…

Q: Test the series for convergence or divergence. E(-1yr (3n – 1). 7n +1 n-1 Evaluate the following…

A: Recall: Divergent theorem,    If limn→∞an≠0, then the given series ∑n=1∞an is divergent. We have,…

Q: Find the four​ second-order partial derivatives for​ f(x, ​y)= 7x4y8 + 8x7y5 Fxx= Fyy= Fxy= Fyx=

A:

Q: In every sphere of radius r it is true that its volume V is given by V =ar³ , A snowball is melting…

A: volume of snowball (sphere);V=43πr3differentiating w.r.t. time t;dVdt=-4π3(3r2) drdtdVdt=-4πr2…

Q: -e elx

A: To evaluate: ∫ex⋅1−e2xdx  I = ∫ex⋅1−e2xdx Let, ex = t ⇒exdx = dt

Q: 10 sin x = 10 + 5 cos x %3D

A:

Q: * What is order of the equation 2y" + 2y +3 = 0 Second order O Third order O First order O Zero…

A: Find the order of the differential equation 2y"+2y+3=0

Q: 3x 4x e, y = e", and Sketch the region enclosed by y = x = 1. Find the area of the region.

A:

Q: Use the dotted line as your y-axis and the solid gray line as the x-axis. Find the distance from the…

A: We need to find area.

Q: Find f, and f, as functions if 2y f(x. y) = y+ y + cos x

A: This question is related to differentiation, We will solve it using given information.

Q: Find the inverse of the function. f(x)= 9 + sqrt 4x -4

A:

Q: lim Max Ax Ef xi Ax, , is equivalent to lim Efa+iAx)Ax with Ax = 5 _b-a 1. The Riemann sum, AX, n00…

A:

Q: Find lim f(x) for the given piecewise function. x→4 2x + 3 if x 4

A: The given function is:

Q: Consider the equation a 4y" + by + cy = 0 the constants a.Gm are real and different from zero, the…

A: To find the inequality between b and c.

Q: Find the average value of f(x) = v9 – x over the interval (0, 3]. Write the exact answer. fave 1…

A:

Q: A graphing calculator is recommended. Find the dimensions that give the largest area for the…

A:

Q: Find the area bounded byf(x)=x^2-4x-5andy=x+1

A:

Q: dy = ky dx

A:

Q: Use a double integral to find the volume under the plane z = 20x + yand over the rectangle R {(x,…

A:

Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 4x + 7 between…

A:

Q: Use the derivative of the function shown below to determine the open intervals in which the function…

A:

Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25 %3D

A:

Q: Find the exponential function that contains the points (2,48) and (3,192).

A:

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A:

Q: Show that the following functions satisfy Laplace's equation dx? = 0. dy? f(x, y) = x³y – ry³

A: Given :f(x,y)=x3y-xy3

Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

A:

Q: Q3. Given the complex numbers z1 = -V3 +i,z2 = 2 - i,z3 = -V3 – 3i and z4 = 4 + 4i 3.1 Represent the…

A: We have to solve given Questions

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x? – 3x + 229, where a…

A: Given; C(x)=0.01x^2-3x+229                R(x)=429-2x

Q: Let D be the region enclosed by y = 5x, y = x and x = 1. The volume of the solid formed by •…

A: Here we have to find the volume .

Q: gths of pregnancies in a small rural village are normally distributed with a mean of s and a…

A: Here the range is 233to 293.  Here I am providing my notes

Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: Set up the definite integral required to find the area of the region between the graph of y = 18 - z…

A:

Q: Describe the graph of the equation. r = - 10i+ (1 – ²)j + t k O It is a parabola in the plane z = –…

A:

Q: dx In x +1+ Vx² + 2x| + C Vx2 + 2x

A:

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: 4 The net signed area in the above graph can be written as (mæ + b)dx, where c = d and b = = U

A: The net signed area in the above graph can be written as ∫cdmx+b dx, where c=?,  d=?m=?, and b=?

Q: 4. Show that a b

A:

Q: Evaluate the limit. 10 lim x→1 х — 1 х2 + 8х — 9 Give your answer in exact form. If the limit does…

A: We have to check limit exist or doesn't exist

Q: Find the volume of a cap of a sphere with radius 50 and height h = 3.

A: volume of sherical cap with radius given r=50 and height=3

Q: Find the area (to three decimal places) bounded byf(x)=x^2e^x and q(x)=4-x^2

A: Given problem:- Find the area (to three decimal places) bounded byf(x)=x2 ex and q(x)=4-x2