That is, T'(1) = %3D

Q: Find the interest earned at 5% compounded continuously for 2 years by a continuous income stream…

A: Given the interest earned r=5%=0.05 , t=2years and PV=1250. We have to find the interest.

Q: Find the derivative. y = e(lnx)2

A: dydx=ddx e(lnx)2        =e(lnx)2 ddx2(ln x)         =e(lnx)2 2x

Q: Find the derivative of the exponential function. Y = x'e-5x dy dx

A:

Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: y = ln 1-x² 1+x²

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: A study of a certain Subanen community suggests thatt years from now, the average level of carbon…

A: Given query is to find the rate of change of carbon monoxide after 2 years.

Q: Locate the relative extrema of y = ln(x2 + 2x + 3).

A:

Q: For any logistic equation, show that the point of inflection occurs at y = L/2 when the solution…

A: Given: The logistic equation

Q: ア=e y =,

A:

Q: If f10,500 is invested fie 3 4ears at a rate of 9%.how much willyou have if interest Es compounded…

A: P=10500t=3 years.r=9%=0.09To find A

Q: Find the derivative of the function. %3D y = log |3- 5x| dy

A: Here , we will differentiate y  with respect to 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: Find the derivative of the function y = log4 (6x + 1)

A: Given information: y=log46x+1 Log rule: logab=lnblna

Q: what is the derivative to y= e^-1?

A: Given,

Q: What happens to the rate of change of the exponential function y = ax as a becomes larger?

A: To explain the given problem

Q: What is the rate of change of y with respect to x for this function?

A:

Q: Find the nth derivative of the function y=ln(ax+b).

A: Given function is Differentiating with respect to x repeatedly, we get In general,

Q: Suppose that $15,000 is invested and at the end of 3 yr, the value of the account is $19,356.92. Use…

A: Given :            $15,000 is invested and at the end of 3 yr, the value of the account is…

Q: Assume that in a certain country, the rate at which jobs are created is proportional to the number…

A: Explanation: Suppose that number of jobs  = N Here given that, the rate at which jobs are created is…

Q: If ω'(t) is the rate of growth of a child in pounds per year,what does  ∫510 ω'(t)  dt   represent?

A:

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: An environmental study of a certain community suggests that t years from now the level L(t) of…

A:

Q: 10 If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does S g'(x)dx…

A: Given, g'(x) is the rate of growth of redwood tree in feet per year now, We have to define…

Q: Find the present value of a continuous income stream F(t) = 40 + 5t, where t is in years and F is in…

A:

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1r dollars per…

A:

Q: b) Find the equation of the line tangent to the graph of y=log; (5x +1) at x = 2

A:

Q: What is the first derivative of s(æ) = 4e"*.

A:

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

A:

Q: Suppose that a community contains 15,000 people who are susceptible to Michaud’s syndrome, a…

A:

Q: (b) Find the derivative of y = log,(5x')+log, (sin.x)

A:

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

A:

Q: Why is the notation dy/dx used to represent the derivative?

A:

Q: find the derivative dy/dx of the functions xlny+ylnx=1

A:

Q: QUESTION 2 Estimate the value of V80.9 + V80.9 using differentials.

A: To evaluate : 80.94 +180.94 Let f(x) = x14 Now, we can write 80.9 = 81- 0.1 Take x=81, ∆x=-0.1

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: Find the linearization of the function k(x) = ln(x) when x= 1 and use it to estimate ln(1.1).

A:

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: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: Find the derivative of the function. y = log |5- 2x dy dx

A:

Q: What is the instantaneous rate of change of A with respect to s when s is 4.00?

A: Given a square of area A in2 and length of the side s in To find the instantaneous rate of change of…

Q: Find the PV of an income stream that pays out continuously at a rate R(t) = $5000e0.1t /year for 7…

A:

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

A: Given: y=lnx at x=1

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

Q: Find the effective annual yield and the continuous growth rate if the value of a deposit is given by…

A: The deposit is given by

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: