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Chapter 7 Solutions
Single Variable Calculus
- Discuss limit(n →∞)fn on B and C for fn(x)=x/n; B=E1; C = [a, b] ⊂ E1 fn(x)=(cos x + nx)/n; B=E1arrow_forwardFind the absolute maximum and absolute minimum of the function f ( x ) = x 2 e -x on the closed interval [ 1 , 4 ].arrow_forwardevaluate the limit: limit of the square root of 1+t - square root of 1-t / t as t approaches 0arrow_forward
- In the function: f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?arrow_forwardIn the function: f(x)= (3x^2)ln(x) , x>0 What are the x-coordinates of all local minima and minima in the function?arrow_forwardFind the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x + 13), [−3, 1]arrow_forward
- Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No 2. Yesarrow_forwarda. Find the critical points of f(x)=x^3-12x-5 and identify the open intervals on which f is increasing and on which f is decreasing b. find lim x arrow infinity (1+1/x)^xarrow_forward5x−12/x^2−x−42 has vertical asymptote(s) at x=arrow_forward
- A process creates a radioactive substance at the rate of 1 g/hr, and the substance decays at an hourly rate equal to 1/10 of the mass present (expressed in grams). Assuming that there are initially 20 g, find the mass S(t) of the substance present at time t, and find lim S(t) as t approaches infinityarrow_forwardLet G(t) = (1 - cos t)/t2. a. Make tables of values of G at values of t that approach t0 = 0 from above and below. Then estimate lim t-->0 G(t). b. Support your conclusion in part (a) by graphing G near t0 = 0arrow_forwardTrue or False. If f(x) is a differentiable function such that f '(-1) = 0, then f(x) either has a local minimum at x = -1 or a local maximum at x = -1.arrow_forward
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