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Calculus: Early Transcendental Functions
- Water Flea F. E Smith has reported on population growth of the water flea. In one experiment, he found that the time t, in days, required to reach a population of N is given by the relation e0.44t=NN0(228N0228N)4.46. Here N0 is the initial population size. If the initial population size is 50, how long is required for the population to grow to 125?arrow_forwardMaximizing profit Suppose a tour guide has a bus that holds amaximum of 100 people. Assume his profit (in dollars) for taking npeople on a city tour is P(n) = n(50 - 0.5n) - 100. (Although Pis defined only for positive integers, treat it as a continuous function.)a. How many people should the guide take on a tour to maximizethe profit?b. Suppose the bus holds a maximum of 45 people. How manypeople should be taken on a tour to maximize the profit?arrow_forwardConsider the attached graph ‚which corresponds to a function h. see the graph in the images According to the graph, the criterion of h corresponds to: a) h(x)= 3cos(x-1)+1 b) h(x)= 3sin(x+1)- c) h(x)= 3sin(x-1)+1 d) h(x)= 3cos(x+1)-1arrow_forward
- Curve Sketching f(x) = x3+3x2-4 Determine if there's any: a.) Critical points b.) The intervals on which f is increasing c.) The intervals on which f is decreasingarrow_forwardlim of x approaching infinity of (e^x-3x)^2 / e^2x+ln(x^2) The (e^x-3x)^2 is on the top of the fraction and the e^2x+ln(x^2) is on the bottom of the fractionarrow_forward1. let f(x)=-3x^2+3x-2 a: find the vertex and if the graph is concave up or down b: the y-int and x-int c: graph d: find the domain and range e: where the graph is increasing and decreasing f: where the f(x)>0 and where f(x)<0arrow_forward
- lim x->0 ((x+k)2 -x2/k)arrow_forwarda. Find the open intervals on which the function is increasing andthose on which it is decreasing.b. Identify the function’s local extreme values, if any, saying where they occur. g(x) = x (ln x)2arrow_forwarda. Find the open intervals on which the function is increasing andthose on which it is decreasing.b. Identify the function’s local extreme values, if any, saying where they occur. g(x) = x2 - 2x - 4 ln xarrow_forward
- Graph f(x) = 2 cos x, g(x) = cos 2x, h(x) = ( f + g)(x) in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-co-ordinates on the graphs of f and g.arrow_forwardF(x)=-4cosx g(x)=2cosx+3 for 0<x<2pi Shade the region on a graph bounded by the graphs of f and g between the points of intersection.arrow_forwardNumerical Methods Use the false position method to find the root value of the following mathematical model or function equation, namely f(x)= ex+3sin x- x log x+4. The guess value or lower limit (xb) and guess or upper limit (xa) can be obtained from the graph. The calculation or iteration is completed if |f(xr)<0,01 or 1% (tolarance value)arrow_forward
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