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Region enclosed by Curves, Inverses, Limits and Derivatives

Problem 1 Find the area of the region enclosed by the curves .... Problem 2 Find a formula for the inverse of the function ..... Problem 3 Find (f-1).... Problem 4 Compute the following limits: ..... Problem 5 Find the derivative of the function y = e^x/1+x .


(See attached file for full problem description with proper equations) --- 1, Differentiate f(x) = e(2x + 5) with respect to x 2, Determine f `(t) if f(t) = G(1- e-kt) 3, Determine f ' (y) if f(y) = exp(3 - ¼ y)

Derivatives of Polynomials and Exponential Functions

I have to understand step by step how to navigate Chapter 3.1 Derivatives of Polynomials and Exponential Functions. However, I don't understand how to get a tangent line from a Y=f (x) if x=a, then use that to find f '(a). I'm given the following: Find equations of the tangent line and normal line to the curve at the give

I need help figuring out this problem.

Initial equation - 100 +10B + 20N - B2 - N2 + 0.5 BN ( B2= B to the secondpower and N2 equals N to the second power) I want to get the first derivative of N so I got this far: 10-2b + .5n =0 .5n=2b -10 N= 4b -20. I can't figure out how they got the answer for N ? Also, why is the number 10 without the B when


Can you please show me how to calculate the following 1. Differentiate f(x) = 1n(5x - 7) with respect to x 2. Obtain the derivative of f(t) = 1n( 5 - 2/3 t)

Inverse functions

Please see problems and show step by step solution in detail please. --- 7.4 Inverse functions Differentiate the problems: 1) f(x) = ln(x^2 + 10) 2) f(à?) = ln(cos à?) 3) f(x) =log2(1-3x) 4) f(x) = 5thROOT(ln x) 5) f(x)=SQRTx * (ln x) 6) f(t) = ln [(2t+1)^3 / (3t-1)^4] 7) h(x)=ln(x + SQRT(x^2-1)) 8) g(x)=ln[(


1.) compute the derivative of f(x)= arctan (x^2) 2.) compute the derivative of f(x)= ln(x^2/(2+x)) 3.) determine an equation for the line tangent to the graph of y= xe^x at the point on the graph were x=2

Derivatives, maxima, minima

1. Find the derivative: f(x) = (x^3-8)^(2/3) 2. Write and equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated value. f(x) = (3x^2 + 5x + 4)(4x + 3), x=0 3. Find the values of any relative extrema: f(x)=1/(x^2-1)


-kt f'(t) if f(t)=G(1-e ) Note (-e is to the square of -kt)


Please solve and explain. Two factories are located at the coordinates (-x,0) and (x,0), with their power supply located at (o,h). Find y such that the total amount of power line from power supply to the factories is a minimum.


Use a graphing utility to graph f and g in the same window and determine which is increasing at the faster rate for "large" values of x. What can you conclude about the rate of growth of the natural logarithmic function? f(x) = ln x, g(x) = the square root of x


1. Suppose f'(t) <0 for all t in the interval (2,8). Explain why f(3) > f(5) 2. Suppose f(0) = 3 and 2 is less than or equal to f'(x) which is less than or equal to 4 for all x in the interval [-5,5]. Determine the greatest and least possible values of f(2).


Find the length and width of a rectangle that has an area of 64 square feet and a minimum perimeter.


Please solve and explain how to do so. Find the point on the graph of the function that is closest to the given point. f(x) = the square root of x Point: (4,0)


Please find the points of inflection and discuss the concavity of the graph of the function. Please explain as much as possible. Please show how to obtain these answers. f(x) = x/x^2 + 1

Determining Concavity in Intervals

For each of the following equations, would you please state the intervals for which it is concave up and for which it is concave down? y = 10xe^-x f(x) = x^2 - 4/x + 1


Please state whether each statement is true or false, and if false please explain why The maximum slope of the graph of y = sin(bx) is b If f''(2) = 0, then the graph of f must have a point of inflection at x = 2.


Please solve and explain to the specified answer. Please explain solution. The deflection D of a particular beam of length L is D = 2x^4 - 5Lx^3 + 3L^2x^2 where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection.