# 1. Find each limit, if it exists. (a) lim x?-1 ?-3 x 4-2×3?5×2?4? (b) lim x? 3 2×2-11x?15 x-3…

1. Experience each season, if it remains. (a) lim x?-1 ?-3 x 4-2x3?5x2?4? (b) lim x? 3 2x2-11x?15 x-3 (c) lim x?-8 6x5?7x3-3x2 1?2x-3x5 (d) lim x?8 3x3?8x?1 3x2-4 (e) lim x? 0 sin?7x? sin? 4x? 2. A rocket is shot undeviating up so that its aspect behind t seconds is abandoned by s?t?=-16t 2?20t?25 (measured in feet). (a) Experience the swiftness for any season t. (b) Experience the succor for any season t. (c) When does the rocket stretch its culmination crisis? 3. Experience the equation of the tangent continuity to the deflexion f ? x ?=4x2-5x?2 at x=1 . 1 4. Experience the derivative of y=x 6-3x5?4x3-2x2?9x?5 5. Evaluate the perfect Y=??10x4-4x3?6x2?3? dx abandoned that Y=5 when x=1 . 6. For f ? x ?= ?2x-5??3x2-2x-8? 6x2-7x-20 , (a) For what x-values is f ? x ? discontinuous? (b) How should f ? x ? be defined to gain it faithful at its discontinuities? That is, redefine f ? x ? as a piecewise, faithful business. 7. Use the specification of the derivative, namely f ' ? x?=lim h?0 f ? x?h?- f ? x ? h , to experience the derivative for f ? x ?= -5 x 2 . 8. For continuity L abandoned by 3x – 2y = 4, (a) What is the arise of the continuity L? (b) What is the arise of any analogous continuity to L? (c) What is the arise of any continuity standing-upright to L? (d) What is the equation of the continuity going through the purpose (5, -1) and standing-upright to continuity L? 2 9. For this piecewise business. g ? x ?={ 3x?1 -4=x?0 x 2-2 0?x=2 -2x?5 x?2 } (a) Graph this business. Now, evaluate the subjoined, or set-forth that the response does not remain. (b) lim x? 2 g ? x ? = _______________________________ (c) lim x?5 g ? x ? = ________________________________ (d) lim x? 0 + g ? x ? = ________________________________ (e) lim x? 0 - g? x ? = ________________________________ (f) g ?2? = ___________________________________ (g) g?0? = ___________________________________ 3 10. Experience the derivatives of the subjoined businesss. Don't worry to simplify! (a) f ? x ?= 2x-3?4x2-7x 5x5-3x3?2x2-1 (b) f ? x ?=? 4x3?7x2-x ??5x4?8x5 ? (c) f ? x ?= sin ? x?tan ? x ? x 2 4
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1. Experience each season, if it remains. 4 3 2 lim ?-3 x -2x ?5x ?4? (a) x?-1 2 2x -11x?15 (b) lim x-3 x?3 5 3 2 6x ?7x -3x (c) lim 5 x?-8 1?2x-3x 3 3x ?8x?1 (d) lim 2 x?8 3x -4 sin?7x? (e) lim sin?4x? x?0 2. A rocket is shot undeviating up so that its aspect behind t seconds is abandoned by 2 (measured in feet). s?t?=-16t ?20t?25 (a) Experience the swiftness for any season t. (b) Experience the succor for any season t. (c) When does the rocket stretch its culmination crisis? 2 3. Experience the equation of the tangent continuity to the deflexion f ?x?=4x -5x?2 at x=1 . 16 5 3 2 4. Experience the derivative of y= x -3x ?4x -2x ?9x?5 4 3 2 5. Evaluate the perfect Y= ?10x -4x ?6x ?3? dx ? abandoned that Y=5 when x=1 . 2 ?2x-5??3x -2x-8? f ? x?= 6. For , 2 6x -7x-20 (a) For what x-values is f ? x? discontinuous? (b) How should f ? x? be defined to gain it faithful at its discontinuities? f ?x? That is, redefine as a piecewise, faithful business. f ? x?h?- f ?x? 7. Use the specification of the derivative, namely f '? x?=lim , to experience h h?0 -5 f ?x?= the derivative for . 2 x 8. For continuity L abandoned by 3x – 2y = 4, (a) What is the arise of the continuity L? (b) What is the arise of any analogous continuity to L? (c) What is the arise of any continuity standing-upright to L? (d) What is the equation of the continuity going through the purpose (5, -1) and standing-upright to continuity L? 29. For this piecewise business. 3x?1 -4=x?0 2 g? x?= x -2 0? x=2 { } -2x?5 x?2 (a) Graph this business. Now, evaluate the subjoined, or set-forth that the response does not remain. lim g?x? (b) = _______________________________ x?2 lim g? x? (c) = ________________________________ x?5 lim g?x? (d) = ________________________________ + x?0 lim g?x? (e) = ________________________________ - x?0 g?2? (f) = ___________________________________ (g) g?0? = ___________________________________ 3