'ind, from first principles, f.(3, –1) for f(x, y) = 4x²y² + e%.

Q: The accumulation function is given by a(t) = (0.01t + 1)^3. What is the force of interest at time t…

A: If the accumulation function is given by a(t) . Then the Force of interest is given by   δt=…

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

A:

Q: What is the amount of salt in the tank at time t = 0?

A:

Q: E) INTEGRAL : 9.) S(5t3 + 2t? – 5t – 50)dt 10.) S(3x2 + 2x + 500)dx

A:

Q: Suppose that z =x*y°,where bothx and y are changing with time. At a certain instant when x = 1 and y…

A: Derivative formula ddxxn= n xn-1Product ruleuv'=u'v+uv'

Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

A:

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: Suppose that z = x*y°, where both x and y are changing with time. At a certain instant when x = 1…

A: For the solution of the problem follow the next step.

Q: A 200-gal tank is half full of distilled water. At time t = 0, a solution containing 0.5 lb /gal of…

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

Q: Determine the average rate of change of the function y = sinx from X = 0 to x = 2 O1 2

A: The average rate of change of the function f(x) can be calculated using the formula Average rate of…

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

Q: At an effective rate of interest i and effective rate of discount d, show that; 1 1 d i

A: The effective rate of interest i is the amount of money that one unit invested at the beginning of a…

Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: Approximate 2x e 2 dx using three equal subintervals. - 1

A: To Approximate

Q: ly 4% confident that the true po ation percentage of people that

A: The margin of error is the amount that is allowed for the error term to vary because of…

Q: Suppose that h = 2x'y, where both x and y are changing with time. At a certain instant when x = 1…

A:

Q: snip

A: Given: fx=3x-5 To Find: The average rate of change of the given function from x=0 to x=4

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: Suppose that z = x²y°, where both x and y are changing with time. At a certain instant when x = 2…

A: Explanation of the answer is as follows

Q: An evolved kind of green fungi is shrinking at an initial rate following f(t) = vVE + 5, where t is…

A:

Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0

A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given : A town predicts that its public school population will decrease at the rate of

Q: What is the period of time ''t'' required for the initial infection rate ''I(t=0)'' to double in…

A:

Q: ex/Eveiluene the fallowing integrels 21/dx XInx

A: The given integrals are 1. ∫dxx1-x2. ∫dxx ln x

Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

A:

Q: Jrin m In(cos m) dm

A:

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: Suppose A is directly proportional to t. Explain what happens to t when A is increased by 5%.

A:

Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

A:

Q: (f) y = e* In(tanh(x))

A:

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: The rate of increase in the number N of bacteria in a certain culture is given by dN = 0.15N where t…

A:

Q: Assume the rate of investment is given by the function I (t) = ln t. Compute the total capital…

A: We solve this problem by using the capital formation i. e. Total capital accumulation=∫t,t2I(t)dt…

Q: Sulve the dffeanlial equalion ly). clox Ylx)=16

A: Given:     dydx+y=16

Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: Use differential to approximate the value e1.01.

A:

Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: Rank the functions x3, ln x, xx, and 2x in order of increasinggrowth rates as x→ ∞.

A: Given x3, ln x, xx, and 2x

Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

A:

Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

A:

Q: What is the rate of change of y = In x at x = 1 O?

A: Given: y=lnx at x=1

Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

A:

Q: dy y(ln y – In a + 1) dx 1 C = -ln C = -In Option 4 O option 2 1 C =-In

A: This question is based on solution of differential equation.

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.