hw04S2 - JAEHYUNPARK Math124,sectionD,Fall2016...

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Unformatted text preview: JAE HYUN PARK Math 124, section D, Fall 2016 Instructor: Dmitriy Drusvyatskiy WebAssign hw04S2.3 (Homework) Current Score : 52 / 52 Due : Friday, October 7 2016 11:59 PM PDT The due date for this assignment is past. Your work can be viewed below, but no changes can be made. Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you have viewed the answer key. Automatic extensions are not granted if you have viewed the answer key. View Key 1. 6/6 points | Previous AnswersSCalcET7 2.3.001. Given that lim f(x) = 9 lim g(x) = −4 lim h(x) = 0, x → 3 x → 3 x → 3 find the limits, if they exist. (If an answer does not exist, enter DNE.) (a) lim [f(x) + 2g(x)] x → 3 1 (b) lim [g(x)]3 x → 3 ­64 (c) lim x → 3 3 f(x) (d) lim x → 3 ­9 4f(x) g(x) g(x) x → 3 h(x) (e) lim DNE g(x)h(x) f(x) x → 3 (f) lim 0 2. 3/3 points | Previous AnswersSCalcET7 2.3.007. Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim 3 + x → 8 3 x 5 − 5x2 + x3 985 3. 3/3 points | Previous AnswersSCalcET7 2.3.011. Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 2 lim x − 4x + 3 x − 3 x → 3 2 4. 5/5 points | Previous AnswersSCalcET7 2.3.012.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x2 − 6x x → 6 x2 − 5x − 6 Part 1 of 3 First, factor the numerator and denominator of lim x2 − 6x x → 6 x2 − 5x − 6 x2 − 6x x2 − 5x − 6 x(x − 6 ) (x − 6 )(x + 1 x → 6 = lim . ) Part 2 of 3 Next, cancel common factors. x(x − 6) = lim x → 6 (x − 6)(x + 1) x → 6 x $$x+1 lim Part 3 of 3 This limit can now be evaluated as follows. (If an answer does not exist, enter DNE.) x = 6/7 x + 1 x → 6 lim You have now completed the Master It. 5. 3/3 points | Previous AnswersSCalcET7 2.3.020. Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.). lim t → 2 t4 − 16 t3 − 8 8/3 6. 3/3 points | Previous AnswersSCalcET7 2.3.029. Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3 lim t → 0 t 1 + t − 3 t ­3/2 7. 5/5 points | Previous AnswersSCalcET7 2.3.047. The signum (or sign) function, denoted by sgn, is defined by sgn x = −1 if x < 0 0 if x = 0 . 1 if x > 0 (a) Sketch the graph of this function. (b) Find each of the following limits. (If an answer does not exist, enter DNE.) (i) lim sgn x x → 0+ 1 (ii) lim sgn x x → 0− ­1 (iii) lim sgn x x → 0 DNE (iv) lim |sgn x| x → 0 1 8. 4/4 points | Previous AnswersSCalcET7 2.3.048. Let f(x) = x2 + 1 if x < 1 (x − 2)2 if x ≥ 1 . (a) Find the following limits. (If an answer does not exist, enter DNE.) lim f(x) = 2 x → 1− lim f(x) = 1 x → 1+ (b) Does lim f(x) exist? x → 1 Yes No (c) Sketch the graph of f. 9. 7/7 points | Previous AnswersSCalcET7 2.3.050. Let x 5 if x < 1 if x = 1 g(x) = . 2 2 − x if 1 < x ≤ 2 x − 1 if x > 2 (a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.) (i) lim g(x) x → 1− 1 (ii) lim g(x) x → 1+ 1 (iii) g(1) 5 (iv) lim g(x) x → 2− ­2 (v) lim g(x) x → 2+ 1 (vi) lim g(x) x → 2 DNE (b) Sketch the graph of g. 10.3/3 points | Previous AnswersSCalcET7 2.TF.002. Determine whether the statement is true or false. lim x2 + 5x − 6 x → 1 x2 + 4x − 5 lim x2 + 5x − 6 = x → 1 lim x2 + 4x − 5 x → 1 True False 11.3/3 points | Previous AnswersSCalcET7 2.TF.003. Determine whether the statement is true or false. lim x → 1 x x − 6 2 + 2x − 4 lim x − 6 = x → 1 lim x2 + 2x − 4 x → 1 True False 12.3/3 points | Previous AnswersSCalcET7 2.TF.015. Determine whether the statement is true or false. If f is continuous at 5 and f(5) = 1 and f(4) = 3, then lim f(4x2 − 11) = 1. x → 2 True False 13.4/4 points | Previous Answers Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x → 8 $$2 12−x − 2 24−x − 4 ...
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