Title Differentiation-1 & Tissue - Daily-10 MCQ (Set-A)-With Solve.pdf ✅

2 e ̈vL ̈v: lim x  0 (1 + 9x) 6 + 3x x = lim x  0 (1 + 9x) 6 x + 3 = lim x  0 (1 + 9x) 6 x . lim x  0 (1 + 9x)3 = lim 9x  0 {(1 + 9x) } 1 9x 96 = e54 kU©KvU: lim x  0 (1 + ax) b x + c = eab 9. x = 2sect, y = 3cost n‡j, dy dx = ? y 2 1 2 x 2 y – 1 6 y 2 xy 2 DËi: – 1 6 y 2 e ̈vL ̈v: dy dt = – 3sin(t) dx dt = 2sec(t)tan(t) dy dx = dy dt dx dt = – 3sin(t) 2sec(t)tan(t) = – 3cos(t) 2sec(t) = – 3 2 cos2 (t) = – 1 6 y 2 10. d dx (e–x ) = ? 1 + x 1! – x 2 2! + x 3 3! – ... 1 – x 1! + x 2 2! – x 3 3! + ... x – x 3 3! + x 5 5! + ... – x 1! – x 2 2 – x 3 3 + ... DËi: 1 + x 1! – x 2 2! + x 3 3! – ... e ̈vL ̈v: Avgiv Rvwb, e –x = 1 – x 1! + x 2 2! – x 3 3! + ......... GLb, d dx (e–x ) = – e –x = 1 + x 1! – x 2 2! + x 3 3! – ......... 11. lim x  0 {4ln(1 + x) + ln(1 + x)} Gi gvb- 0 1 2  DËi: 0 e ̈vL ̈v: lim x  0 {4ln(1 + x) + ln(1 + x)} = 4ln(1 + 0) + ln(1 + 0) [wjwgU ewm‡q] = 4  ln1 + ln1 = 0 + 0 = 0 12. lim x  0 e 3sinx – 1 2sinx = ? e 3 2 ln 3 2 3 2 2 3 DËi: 3 2 e ̈vL ̈v: lim x  0 e 3sinx – 1 2sinx = lim x  0 e 3sinx  3cosx 2cosx [Using L' Hôpital] = e 0  3 2 = 3 2 13. lim x  –  x 2 + 2x – x = ? – 1 1 1 2 0 DËi: 1 e ̈vL ̈v: lim x  –  x 2 + 2x – x = lim x  –  – x 1 + 2 x – x = 1 = 1 14. e sincos–1 2x Gi AšÍiR †KvbwU? 4xe 1 – 4x2 1 – 4x2 4e 1 – 4x2 1 – 4x2 e 1 – 4x2 – 4xe 1 – 4x2 1 – 4x2 DËi: – 4xe 1 – 4x2 1 – 4x2 e ̈vL ̈v: e sincos–1 2x = e sinsin–1 1 – 4x2 = e 1 – 4x2 d dx e 1 – 4x2 = e 1 – 4x2 . 1 2 1 – 4x2  (– 8x) = – 4xe 1 – 4x2 1 – 4x2 15. y = log    tan x 2 n‡j, dy dx = KZ? secx cosecx cotx cosx DËi: cosecx