imt→∞31 + t2 .(a) 0 (b) 1 (c) 2 (d) 3 (e) The limit does not exist[22]. Find the limit limx→∞x2 + x + 1(3x + 2)2 .(a) 1 (b) 1/3 (c) 0 (d) 1/9 (e) The limit does not exist[23]. Find the limit lims→∞s4 + s2 + 13s3 + 8s + 9 .(a) 0 (b) 1 (c) 2 (d) 3 (e) The limit does not exist36
Question
imt→∞31 + t2 .(a) 0 (b) 1 (c) 2 (d) 3 (e) The limit does not exist[22]. Find the limit limx→∞x2 + x + 1(3x + 2)2 .(a) 1 (b) 1/3 (c) 0 (d) 1/9 (e) The limit does not exist[23]. Find the limit lims→∞s4 + s2 + 13s3 + 8s + 9 .(a) 0 (b) 1 (c) 2 (d) 3 (e) The limit does not exist36
Solution
For the first question, we need to find the limit as t approaches infinity of the expression 31 + t^2. To do this, we can observe that as t becomes larger and larger, the t^2 term will dominate the expression. Therefore, the limit will be infinity. So the answer is (e) The limit does not exist.
For the second question, we need to find the limit as x approaches infinity of the expression (x^2 + x + 1)/(3x + 2)^2. To simplify this expression, we can divide both the numerator and denominator by x^2. This gives us (1 + 1/x + 1/x^2)/(9 + 12/x + 4/x^2). As x approaches infinity, the terms with 1/x and 1/x^2 become smaller and smaller, approaching zero. Therefore, the limit simplifies to 1/9. So the answer is (d) 1/9.
For the third question, we need to find the limit as s approaches infinity of the expression s^4 + s^2 + 13s^3 + 8s + 9. As s becomes larger and larger, the highest power term, s^4, will dominate the expression. Therefore, the limit will be infinity. So the answer is (e) The limit does not exist.
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