When demonstrating that lim 4r+4=-4 with e =0.1, which of the following &-values suffices? T -2 [There may be MORE THAN ONE correct answer, so select all that apply] 80.0083333333333333 8 =0.05 C. 8=0.000625 D. 8 =0.025 A. В.
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- a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.Note: You may need to assume the fact that lim M→+∞ Mne−M = 0 for all n.Sales of the text Calculus and You have been declining continuously at a rate of 2% per year. Assuming that Calculus and You currently sells 4,700 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. HINT [Use a model of the form Aert.]Find the Indicated Limit Limh-0(4h5-20h2+2h+1)
- Given that lim x→4 (4x − 13) = 3, illustrate Definition 2 by finding values of delta that correspond to epsilon = 0.1, epsilon = 0.05, and epsilon = 0.01. epsilon = 0.1 delta≤ epsilon = 0.05 delta≤ epsilon = 0.01 delta≤Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.4. Find Lim?→0^+ (1/(e^x - 1) - 1/x)
- Find the following limits: (a) If lim x--> 3 ((?f(x)/2x) +1)?=2,find lim x→3 f(x) (b) Find lim x→0 tan(4x)/sin(6x) (c) Evaluate lim x→∞ (-2x^3-2x+3)/(3x^(3)+3x^(2)-3) Answers should be written as √2 as opposed to 1.4142135. Also please show your work step by step.n is not a negative integer Given n ≥ 0; justify that limx->∞ fn (x) / ex = 0Find the following limits. limx->+infinity (sin2x)/(x2+1) limx->+infinity (e-2x cosx) limx->+infinity (e-x+2cos3x)
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