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Free-Falling Object In Exercises 37 and 38. use the position function
Find the velocity of the object when
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Chapter 1 Solutions
Calculus
- lim(x,y) aproaches (0,0) (3x3y)/(x6+y2)arrow_forwardPopulation growth Consider the following populationfunctions.a. Find the instantaneous growth rate of the population, for t Ú 0.b. What is the instantaneous growth rate at t = 5?c. Estimate the time when the instantaneous growth rate is greatest.d. Evaluate and interpret limtS∞ p(t). Use a graphing utility to graph the population and its growth ratearrow_forward12. Consider that the inflation rate in a six-year period in Mexico behaves according to the function i(T)=t^2 - t + 3Calculate the minimum value of inflation and the time in which it reaches this value. Consider the domain of the function [0,6] and the time in years. Provide the graphic behavior of inflation during the six-year period.In what interval does I(+) decrease? That is, there is deflation.arrow_forward
- Mymathlab homework for business calculus: Use f'(x)= lim h-->0 f(x+h)-f(x)/h to find the derivative at x for the given function. s(x)=5x+8, s'(x)=?arrow_forwardLinearizations at inflection points Show that if the graph of a twice-dierentiable function ƒ(x) has an inflection point at x = a, then the linearization of ƒ at x = a is also the quadratic approximation of ƒ at x = a. This explains why tangent lines fit so well at inflection points.arrow_forwardEstimating changes with linear approximationsa. Approximate the change in y = ƒ(x) = x9 - 2x + 1 when x changes from 1.00to 1.05.b. Approximate the change in the surface area of a spherical hot-air balloon when the radius decreases from 4 m to 3.9 m.arrow_forward
- lim ilm f(x,y)=x²y²÷x²y² Calculate the two limits of the functionarrow_forwarda. Show that if the position x of a moving point is given by a quadratic function of t, x = At2 + Bt + C, then the average velocity over any time interval [t1, t2] is equal to the instan-taneous velocity at the midpoint of the time interval. b. What is the geometric significance of the result in part (a)?arrow_forwardFind an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the equation. f′(x) = (y0 − y)/(x0 − x) f(x) = √x, (x0, y0) = (−4, 0)arrow_forward
- Calculus I In the exercise f(x)= cos x + sin x; [0,2pi], find the following 1.) Search for critical points2.) Search if it grows or decreases3.) Search for local maximum and minimumarrow_forwardApplication of Differential Calculus: Optimization Farmers use a certain plant food costing $4.00 per ounce to help them in growing oranges. It is estimated that when x ounces of the food are used on an ace of orange grove, the farmer is able to get Ln(4x+5) crates of oranges from that acre of land. If the farmer can sell the oranges at $20 per crate, how many ounces should be used per acre to maximize the orange crops net value.arrow_forwardlim y approaches 2 ............. [y^3 - 8]/[y^4 - 16]arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning