Title Tutorial6 Final MAT183.pdf ✅

Tutorial 6: Differentials/Linear Approximation MAT183 (Calculus I) Mahani@Feb25 31 1. If f(x) = x 3√5 − x 2 find the differential df. Hence, estimate the value of (1.05) 3√5 − (1.05) 2. [Mar04] 2.275 2. Use differentials to estimate √1.02 + √1.02 3 to four decimal places. [Oct04] 2.0167 3. Use differentials to estimate (49.02) 3 2 − (49.02) 1 2 −8. Give your answer correct to two (2) decimal places. [Nov05] 328.21 4. Use differentials to estimate √9.03 + 1 √9.03 to three (3) decimal places. [Apr06] 3.338 5. Use differentials to estimate √14.8 4 correct to three (3) decimal places. [Oct06] 1.963 6. Given f(x) = √25 − x 2. Use differential to estimate the value of √25 − (2.9) 2. Give your answer correct to three (3) decimal places. [Apr07] 4.075 7. Use differentials to approximate (16.02) 3 2 + 2√16.02. Give your answer to 3 decimal places. [Oct07] 72.125 8. Use differentials to approximate √1 + ln(1.1) correct to two (2) decimal places [Apr08] 1.05 9. Use differentials to estimate f(2.9) given that f(3)=3 and f ′ (x) = x √x 2−1 3 . [Oct08] 2.85 10. Estimate the value of 1 √9.025 using differentials. Give your answer to 4 decimal places. [Apr09] 0.3329
Tutorial 6: Differentials/Linear Approximation MAT183 (Calculus I) Mahani@Feb25 32 11. Estimate the value of √1 + 0.9 using differentials. Give your answer to 3 decimal places. [Oct09] 1.378 12. Use differentials to approximate √124 3 . Give your answer to three (3) decimal places. [Apr10] 4.987 13. Use differentials to estimate sin ( π 5 + 0.01) correct to four (4) decimal places. [Oct10] 0.5959 14. Use differentials to estimate the value of √36.02 and give your answer correct to four decimal places. [Apr11] 6.0017 15. Given f(x) = √20 − x 2, use differential to estimate the value of √20 − (1.99) 2 . Give your answer correct to three (3) decimal places. [Sep11] 4.005 16. Use differentials to estimate the value of √7.96 3 correct to four (4) decimal places. [Mar12] 1.9967 17. Given f(x) = √4x 2 − 7. Estimate the value of f(2.01) using differential. Give your answer correct to three (3) decimal places. [Oct12] 3.027 18. Estimate the value of √16.03 + 4 √16.03 4 using differentials. Give your answer correct to three (3) decimal places. [Mar13] 6.033 19. Use differentials to estimate the value of √15.95 4 correct to four (4) decimal places. [Sep13] 1.998 20. Use differentials to estimate the value of √63.8 − √63.8 3 to three decimal places. [Mar16] 3.992
Tutorial 6: Differentials/Linear Approximation MAT183 (Calculus I) Mahani@Feb25 33 21. Use differentials to estimate the value of (15.99) 3 4 + (15.99) 1 2 to three decimal places. [Oct16] 11.995 22. Use differentials to estimate the value of √63.99 3 + 1 √63.99 to three decimal places. [Mar17] 4.125 23. Given f(x) = 8 x 3 + ln(2x − 3). Estimate the value of f(2.01) using differentials. [Jan18] 1.005 24. Use differentials to estimate √63.99 − 2 √63.99 3 correct to four decimal places. [Jun18] 7.4493 25. Use differentials to estimate √3.99 + (3.99) 3 correct to two decimal places. [Dec18] 65.52 26. Use differentials to estimate the value of ln(0.98) + (0.98) 5 . [Jun19] 0.88 27. Use differentials to estimate the value of √15.8 − 2 √15.8 4 correct to four decimal places. [Dec19] 2.9719 28. Use differentials to estimate the value of √15.98 4 − ( 15.98 4 ) 2 correct to four decimal places. [Feb23] −13.9606 29. Use differentials to estimate the value of (4.01) 3 − 1 √4.01 correct to three decimal places. [Jul23] 63.981 30. Use differentials to estimate the value of (4.02) 2 − ln(4.02) correct to three decimal places. [Jan24] 14.769
Tutorial 6: Differentials/Linear Approximation MAT183 (Calculus I) Mahani@Feb25 34 31. Use differentials to estimate the value of √7.99 3 + (7.99) 2 correct to three decimal places. [Jul24] 65.839 32. Use linear approximation to estimate the value of √63.8 − 3 √63.8 3 correct to four decimal places. [Feb25] 7.2367