2. Why is the natural logarithmic function y = ln x used more often in calculus then the other logarithmic functions y=loga x ?
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2. Why is the natural logarithmic function y = ln x used more often in calculus...
The exponential function V-e increases on the interval The logarithmic function y = ln ( x) increases on the interval By definition, In(e) Hence, for all x >0 it follows that Ine-1)< In(e-1 and we immediately have thatx201x0 for all x>0 2.01 Since is a p-series with p- /n In (e"-1 by direct comparison, we conclude that 2.01 3b: Complete the outline to verify the convergence or divergence of the infinite series using limit comparison. In(e-1 and b" and then...
(point) Match each logarithmic function f(x) with its graph. 1.f(x) = ln(-x) 2.f(x) = - In(-x) 3.f(x) = - In(x) 4. f(x) = ln(x - 6) 5. f(x) = 6 + In(x) 6.f(x) = In(6 - x)
Use logarithmic differentiation to find the derivative of the function. y = (tan(x))2/ 4 cos ec(2x) y' = 2 ln(tan(x)) 2 Need Help? Read It Watch It Talk to a Tutor Submit Answer 13. [1/1 Pointsi TOT
# 2,3,4,7, 10,11,15,18) Differentiate the function: #2 f(x) = ln(22 + 1) #3 f@) = ln(cos) #4 f(x) = cos(In x) #7 f(x) = log2(1 – 3x) #10 f(t) = 1+Int #11 F(x) = In( 3+1") #18 y = (ln(1 + e*)] # 23) Find an equation of the tangent line to the curve y = In(x2 – 3) at the point (2,0). # 27, 31) Use the logarithmic differentiation to find the derivative of the function. # 27 y...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
answer for a has to include ln → = EXPONENTIAL AND LOGARITHMIC FUNCTIONS Writing and evaluating a function modeling continuous... At the beginning of a study, a certain culture of bacteria has a population of 80. The population grows according to a continuous exponential growth model. After 7 days, there are 216 bacteria Dino lo X 5 (a) Lett be the time (in days) since the beginning of the study, and let y be the number of bacteria at time...
O EXPONENTIAL AND LOGARITHMIC FUNCTIONS Solving a multi-step equation involving natural logarithms Solve for x. 2+ In (x-5) = 5 Do not round any intermediate computations, and round your answer to the nearest hundredth. x = Х ? Solve for x. 2+ In(x-5) = 5 Do not round any intermediate com
= O EXPONENTIAL AND LOGARITHMIC FUNCTIONS Solving a multi-step equation involving natural logarithms Solve for x. 2 + In (x-5) = 5 Do not round any intermediate computations, and round your answer to x = X 5 ?
3. (a) Write a MatLab program that calculates for the function F(x, y) = ln(x + Va,2-y2) The program should use pretty) to display both the original function and the differentiated result, and also use fprintf() to print a label such as "F(x,y) -" and "dF/dxdy - " in front of both the function and the derivative. Then have your program also print out the derivative again after it uses simplify() on the result (b) Find the Taylor expansion of...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z Problem 4 (a) Derive the demand functions for the utility function (b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the...