If z = (x + y)e", x = 4t, y = 5-t², find dz/dt using the chain rule. Assume the variables are restricted to domains on which the functions are defined. =

Q: Determine whether the given function is a solution to the given differential equation. d²e de dt² dt…

A: Given the function  θ=3e5t-5e2t we need to calculate if this is a solution of the given…

Q: Find the cross product a x b. a(t, 2, 1/t), b =(², ², 1) Verify that it is orthogonal to both a and…

A:

Q: Solve each equation. 3) 6-6-3-3

A: We need to solve: 6-n=6-3n+3

Q: A particle moves along x - axis and the differential equation governing the motion of the particle…

A: Given differential equation is 4(d2x/dt2)=-16x-16(dx/dt)  We have to find the value of x(t)

Q: Solve the initial value problem. y'+xy=x , y(0)=1

A: Given data y'+xy=x , y(0)=1

Q: If 2000 square centimeters of material the largest possible volume of the box. Volume = available to…

A: Surface area = 2000 cm2 Box description÷ Square base and open top Let the square base have length of…

Q: 3.. Compute the arc length of r(0) = 2+2sinə in exact form.

A: Solving the problem.

Q: A chemist, running tests on an unknown sample from an illegal waste dump, isolates 61 grams of what…

A: Given: Initial amount=61g Final amount=12g  Time=66days

Q: (b) You walk in a straight line away from a speaker. Suppose the volume of the sound, Vin decibels,…

A: You walk in a straight line away from a speaker. Suppose the volume of the sound, V in decibels, is…

Q: Find the area between the curves. x = -5₁ x = 3, y = 2x² + 5, y = 0

A: The equation of curves are: x=-5, x=3, y=2x2+5 and y=0 To determine: The area between the curves.

Q: S²10 f(x) dx = -10, Use these values to evaluate the given definite integrals. 2 1) ²³ (f(x) + g(x))…

A:

Q: y lim f(x) = -∞ X-a- (B) a -X lim f(x) = +00 X-a+

A:

Q: Growth of Bacteria Under a set of controlled laboratory conditions, the size of the population of a…

A: give bacteria growth function f(t)=3t2+2t+1

Q: Consider the one-parameter family of functions given by g(x) = xe¹ - Ax where A > 0. (a) Find g(x) -…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 6. Assume x and y are functions of t. Evaluate dy for 2xy-3x+3y=-45, with the conditions dt dx dt…

A: The equation of the curve is 2xy-3x+3y3 =-45               ........1 The conditions are: dxdt =-12,…

Q: Solve 24-4x²³/dx + xdy = 0 using the integrating factor M = 2² SPOXK

A: Solve 2(y - 4x2)dx +x dy=0, Using the integrating factor μ=e∫P(x) dx.

Q: 1 P√P H dz

A:

Q: Part II. Indicate where the following quadratic functions direct the concavity. 1) y=-3x²+2x-5…

A: We must locate the second derivatives of the following quadratic functions and examine their signs…

Q: Evaluate arcsin (3). Give your answer in exact form (no decimal equivalents).

A:

Q: dy (a) Show that y*+x-4 = 0 is an implicit solution to dx on the interval (-∞0,4).

A: To show that y4+x-4=0 is an implicit solution  to dydx=-14y3 on the interval -∞, 4. Note: Since the…

Q: (a) Find symmetric equations for the line that passes through the point (2, -2, 7) and is parallel…

A:

Q: Suppose 4x² +9y² = 100, where x and y are functions of t. dx dy 1 dt 3 dt (a) If dx dt = (b) If dx…

A: Suppose 4x2+9y2 =100, where x and y are functions of t.  a) If dydt=13, find dxdt when x= 4 and y=2…

Q: Question #9 - Which statement is false about the integral 4x dx 7 B a) This is a definite integral…

A: Given that integral is  Ans - (e) is false statement

Q: 20) Find the function f(x) if f'(x) = 2x³ +1 and f(2)=4

A: given f'(x)=2x3+1 and f(2)=4

Q: 8. For the curve given by r(t) = (2 cos(t), 2 sin(t), 2t +), find (a) the unit tangent vector (b)…

A:

Q: Find the equation of the line that is tangent to the hyperbola at the given point. Write your answer…

A:

Q: Find 3e dx f3e³ + C

A: ∫3exdx: Here taking constant out.   ∫afxdx=a·∫fxdx      =3∫exdx

Q: Use the graph to find the following limits. (a) lim f(x) (b) lim f(x) x -3 x--1 (a) Find lim f(x) or…

A: limx→cf(x)=L if and only iflimx→c-f(x)=limx→c+f(x)=L

Q: Evaluate the definite integral. 3 f √3x + 16 dx

A:

Q: The partially completed table below shows the ten basic solutions to the following e-system. = 29 =…

A:

Q: 4. Determine whether the given functions f(x) and g(x) are inverses of one another. Justify your…

A:

Q: A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the…

A: In this question , we will find the dimensions of the box.

Q: Use the price-demand function below, to answer parts (A). (B), and (C) p(x)=90-3x (A) What is the…

A: The price-demand function is given below. px=90-3x, 1≤x≤25 (A) To find the revenue function. To find…

Q: The ramp of a moving truck touches the ground 15 feet away from the end of the truck. If the ramp…

A: The ramp of a moving truck touches the ground 15 feet away from the end of the truck. If the ramp…

Q: 3 1 13. Jisc(2)csc (2x)cot (2x)dx cresc 8 Type. U = U' =

A:

Q: Evaluate the definite integral 7 Li (2x + 5) dx

A:

Q: Solve the initial value problem below for the Cauchy-Euler equation. ty"(t)-6ty' (t)+12y(t) = 0;…

A:

Q: Find equation of the tangent line T equals pi divided by six at X(T) equals nine cosine t and  Y(T…

A: x(t)=9cost y(t)=5sint t=π/6

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Consider

Q: Find the interest rate needed for an investment of $5,000 to grow to $7,000 in 6 years if interest…

A:

Q: 1. The curves y = x and y = x sin(x) are graphed below. Find the area of the shaded re bounded…

A:

Q: Explain the meaning (by using intuitive definition) of each of the following equations. tan x (a).…

A: Given,limx→0 tan(x)x = 1we need to explain how we get this.as x→0 , tan(x)→0 and x =0 so, we get the…

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 00 n14 n=1…

A:

Q: (a) In each case, determine if L'Hopital's Rule applies. 3x lim x-0+ 3x - 1 √t + et lim t-00 In(t)…

A: We need to find the L-Hospital's rule that applies to calculate the limit:…

Q: 2. Write the equation of the tangent line for the function r=4 sin(40) at the value =

A:

Q: NJ 2 AY 4 X

A:

Q: Suppose that a population grows according to the unlimited growth model described by the dy…

A:

Q: 7a. Find the Taylor Polynomial P3(x) that uses a Taylor Series centered around x=3 to approximate…

A:

Q: Solve (D2+20D+200)y = 10 O y = e-10x (c₁sin10x + c₂cos10x) + 20 Oy=e-10x (c1sin10x + c₂cos10x) +…

A: Given

Q: (1) 8 n=1 n³+n²

A: