Essential Calculus
2nd Edition
ISBN: 9781285209067
Author: Stewart
Publisher: Cengage
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Suppose that lim x→0f(x)/x = 3. Thenlim x→−1f(x^2 + x)/(x^2 − x − 2) =(a) = −1 (b) = 1 (c) = 0 (d) does not exist (e) none of these
Find the following limits : 3 1 lim oy
Let f(x, y) = (x2)/(x4+y). Show that Lim (x,y)→(0,0)f(x, y) does not exist.Hint: Consider y = kx2 for different values of k.
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- 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≤arrow_forwardEvaluate the following limits at infinity. Justify your results. arrow_forward1. Write a proof for each of the following limits (Show your scratchwork before starting withthe proof):(i) limx→1x2 + 2x + 12x − 3= −4(ii) limx→−2(x3 − 5x2 − x − 2) = −28.(iii) limx→2√x2 + 1 =√5.arrow_forward
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