Test I. Multiple Choice: Solve for the limit and circle the letter of the correct answer. lim_(x rarr3)(x+2) A. 1 B. 2 C. 7 D. 5 lim_(x rarr7)((x+1)/(2)) A. 3 B. 5 C. 4 D. 2 lim_(x rarr11)(sqrt(x-2)) A. 3 B. 2 C. 4 D. 6 lim_(x rarr1)((x+5)/(x+2)) A، 1 B. 2 C. 7 D. 3 lim_(x rarr3)(x^(2)+5x-7) A. 13 B. 12 C. 17 D. 16 lim_(x rarr2)(x^(2)+5x-1) A. 11 B. 12 C. 13 D. 14 lim_(x rarr1)(2x^(2)+3x-2) A. 2 B. 3 C. 4 D. 5 lim_(x rarr5)(x-8) A. 11 B. 12 C. 13 D. 14 lim_(x rarr3)(x^(2)-x-3) A. 3 B. -2 C. -3 D. 2 lim_(x rarr3)((x^(2)-9)/(x-3)) A. 3 B. 4 C. 5 D. 6 lim_(x rarr6)(x-10) A. 4 B. -4 C. -5 D. 5 lim_(x rarr-2)(x^(2)+5x-7) A. 7 B. -7 C. -6 D. 6 lim_(x rarr6)((x^(2)-36)/(x-6)) A. 13 B. -13 C. 12 D. -12 lim_(x rarr4)(3x-10) A. -3 B. -2 C. 2 D. 3
Question
173
Answer
4.1(210 votes)
Marie RamosExpert · Tutor for 3 years
Answer
<p> 1.C 2.C 3.A 4.B 5.C 6.D 7.B 8.C 9.B 10.D 11.B 12.D 13.C 14.C</p>
Explanation
<p> To solve each limit, we apply the direct substitution method, which involves substituting the value to which x approaches directly into the function if the function is continuous at that point. This method is straightforward for these problems since they all involve algebraic expressions where direct substitution gives a finite number.<br />1. Substitute x = 3 into \(x + 2\) to get 5.<br />2. Substitute x = 7 into \(\frac{x + 1}{2}\) to get 4.<br />3. Substitute x = 11 into \(\sqrt{x - 2}\) to get 3.<br />4. Substitute x = 1 into \(\frac{x + 5}{x + 2}\) to get 2.<br />5. Substitute x = 3 into \(x^2 + 5x - 7\) to get 17.<br />6. Substitute x = 2 into \(x^2 + 5x - 1\) to get 15.<br />7. Substitute x = 1 into \(2x^2 + 3x - 2\) to get 3.<br />8. Substitute x = 5 into \(x - 8\) to get -3.<br />9. Substitute x = 3 into \(x^2 - x - 3\) to get 3.<br />10. The expression \(\frac{x^2 - 9}{x - 3}\) simplifies to \(\frac{(x - 3)(x + 3)}{x - 3}\), which further simplifies to \(x + 3\) after canceling \(x - 3\), so substituting x = 3 gives 6.<br />11. Substitute x = 6 into \(x - 10\) to get -4.<br />12. Substitute x = -2 into \(x^2 + 5x - 7\) to get 3.<br />13. The expression \(\frac{x^2 - 36}{x - 6}\) simplifies to \(\frac{(x - 6)(x + 6)}{x - 6}\), which further simplifies to \(x + 6\) after canceling \(x - 6\), so substituting x = 6 gives 12.<br />14. Substitute x = 4 into \(3x - 10\) to get 2.</p>
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