想問問有大神會這一題嗎？老師的字比較藝術

Let f(x) = {xsin = ²₁ x+0 k H x=0.1元 Determine the value of a such that fox continuous at f(x) x=0.

求解25、29跟32

108 13. lim 15. lim 17. lim 19. lim 818 21. lim x18 CHAPTER 2 23. lim 31² + aitab od n61² + 1 - 5 lin 1³ - 4t + 1 14. lim 9-2/² n r - p³ 2² + 3r³ 4-√√√x 2 + √√x √x + 3x² 4x 1 √1 + 4x6 2-x² (12 saior,558) 2x5 - X x→→∞ x² + 3 26. lim (√x² + ax X-8 27. lim (x - √x) x →8 25. lim (√25t² + 2 − 5t) 1900 29. lim (e-2x cos x) X18 31. lim esec x X→(π/2) + - L 33. (a) For f(r) = LIMITS AND DERIVATIVES OT32 X M mbinogest 20 16. lim 18. 3x³8x + 2 x→∞ 4x²³5x² - 2 20. lim 1-8 lim →20 22. lim 8118 yd boonlqs ei 24. lim √x² + bx) 32. lim [ln(1 + x²) − In(1+x)] - x18 (u² + 1)(2u² - (u² + 2)² t + 3 odme 30. lim √21² - 1 √√1 + 4x6 2 - x² ledre att n q³ + 69 - 4 q→∞ 4q² − 3q + 3 SO 28. lim (x² + 2x²) 8118 1- e* *→∞ 1 + 2e*

求解 微積分

Example 4. Find lim xecos 1 T-0 0 ≤|cos | ≤1 => e«el cos 12 E °° lim x ²³ e ²° = 0 and I'm x ²e²=0 X70 X-0 Cost Ee =0 by

求b小題

dt' Find the equations of the tangent and normal line at the indicated point. (a) x² + y² = 169, (5, 12) (b) z² + z tan ¹y=y> 1, (−1)

微積分求救！

MGT Calculus Homework Assignment 3 5. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, given an example to show why it is false. If f(x) = πª, then f'(x) = xπª-¹. False 7 [$3.1 - 77] 6. F

想請問第59.61題要怎麼算？求解🙏🥹

59. lim Ax-0 61. lim Ax-0 62. lim Ax-0 2(x + Ax) - 2x Ax DAIWS 60. lim (x + Ax)³ = x³ Ax Ax-0 (x + Ax)² - x² Ax odi (x + Ax)² = 2(x + Ax) + 1 - (x² - 2x + 1) Ax niz x angemi ya

想問一下這題 因為課本沒有解答也不知道自己算得對不對

16. Chemistry: Wind Chill At 0° Celsius, the heat loss H (in kilocalories per square meter per hour) from a person's body can be modeled by notenui ent to VID N ov x3 ml H = 33(10√v − v + 10.45) where v is the wind speed (in meters per second). dH (a) Find and interpret its meaning in this situation. dv zive (b) Find the instantaneous rates of change of H when v = 2 and v 5. =

（大一微積分） 請問這題這樣寫正確嗎？背流程寫的😅，圖一為需用到的定義 正確的話，想問紅色圈圈的1是怎麼來的？

DEFINITION Let f be a function defined on some open interval that con- tains the number a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a is L, and we write lim f(x) = L x→a if for every number &> 0 there is a corresponding number 8 >0 such that | ƒ(x) − L| < ɛ if 0 < x-a <8 then

三角函數微積分請益 謝謝🙏

sin 8x cos 5x dx

求解答，二變數函數的偏微分

du 2. u=x² * (1) x (2) du dy du (3) dz